2024 Function concave up and down calculator

The graph of a function f is concave up when f ′ is increasing. That means as one looks at a concave up graph from left to right, the slopes of the tangent lines will be increasing. Consider Figure 3.4.1 (a), where a concave up graph is shown along with some tangent lines. Notice how the tangent line on the left is steep, downward, corresponding to a …. David venable net worth

To find the interval where the function is concave up, we need to determine the values of x for which the second derivative of the function is positive. Step 7/8 Find the interval where the function is concave down.However, not all graphs are straight lines; they may bend up or down. ... Figure 6.1: Graph of salary function is concave up ... Evaluate without a calculator: (a) ...This video defines concavity using the simple idea of cave up and cave down, and then moves towards the definition using tangents. You can find part 2 here, ...Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-stepConcave up (also called convex) or concave down are descriptions for a graph, or part of a graph: A concave up graph looks roughly like the letter U. A concave down graph is shaped like an upside down U (“⋒”). They tell us something about the shape of a graph, or more specifically, how it bends. That kind of information is useful when it ...Consequently, to determine the intervals where a function $f$ is concave up and concave down, we look for those values of $x$ where $f''(x)=0$ or $f''(x)$ is undefined. When we have determined these points, we divide the domain of $f$ into smaller intervals and determine the sign of $f''$ over each of these smaller intervals. If $f ...Question: 4 Consider the function f(x)=ax3+bx where a>0. (a) Consider b>0. i. Find the x-intercepts. ii. Find the intervals on which f is increasing and decreasing. iii. Identify any local extrema. iv. Find the intervals on which f is concave up and concave down. (b) Consider b<0. i. Find the x-intercepts. ii. Find the intervals on which f is ...The fact that its derivative, \(f'\text{,}$ is decreasing makes $f$ concave down on the interval. Figure $\PageIndex{7}$. At left, a function that is concave up; at right, one that is concave down. We state these most recent observations formally as the definitions of the terms concave up and concave down.Concavity of graphs of functions - Concave up and down. New Resources. Construct a Conic; Kopie von parabel - parabol; alg2_05_05_01_applet_exp_flvsFor the following functions, (i) determine all open intervals where f (x) is increasing, decreasing, concave up, and concave down, and (ii) find all local maxima, local minima, and inflection points. Give all answers exactly, not as numerical approximations. (a) f (x)= x-2sinx for -2? < x < 2? There are 2 steps to solve this one.If a function is bent upwards, it’s referred to as concave up. Conversely, if it bends downward, it’s concave down. The point of inflection is where this change in bending direction takes place. Understanding the concavity function is pivotal, especially when we’re on the lookout for inflection points. How to Find Concavity?Calculus. Find the Concavity f (x)=x^4-4x^3+2. f(x) = x4 - 4x3 + 2. Find the x values where the second derivative is equal to 0. Tap for more steps... x = 0, 2. The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.When I took calculus, we didn't use "concave" and "convex" - rather, we (and the AP exam) used "concave up" and "concave down." I still use these as a grad student. ... One can also remember that concave functions look like the opening of a cave. Share. Cite. Follow answered Jul 19, 2017 at 17:29. Sean Roberson ...For the following function determine: a. intervals where f f f is increasing or decreasing b. local minima and maxima of f f f c. intervals where f f f is concave up and concave down, and d. the inflection points of f f f. f (x) = x 4 − 6 x 3 f(x)=x^{4}-6 x^{3} f (x) = x 4 − 6 x 3Determine the intervals on which the given function is concave up or down and find the points of inflection. f(x) = (x^2 - 10)e^x; Determine the intervals on which the function is concave up or down and find the points of inflection. y=xe^(-3x) Determine the intervals on which the function is concave up or down and find the points of inflection.About this unit. The first and the second derivative of a function give us all sorts of useful information about that function's behavior. The first derivative tells us where a function increases or decreases or has a maximum or minimum value; the second derivative tells us where a function is concave up or down and where it has inflection points.The Function Calculator is a tool used to analyze functions. It can find the following for a function: parity, domain, range, intercepts, critical points, intervals of increase/decrease, local and global extrema, concavity intervals, inflection points, derivative, integral, asymptotes, and limit. The calculator will also plot the function's graph.Math. Calculus. Calculus questions and answers. Determine where the given function is concave up and where it is concave down. f (x)=x3+3x2−x−24 Concave up on (−∞,−1), concave down on (−1,∞) Concave down on (−∞,−1) and (1,∞), concave up on (−1,1) Concave up on (−1,∞), concave down on (−∞,−1) Concave down for all x.Something that goes from standing still to moving must be speeding up, so just to the right of each of t = 1 t = 1 and t = 3 t = 3 should count as speeding up. Conversely, just to the left of each of t = 1 t = 1 and t = 3 t = 3 the particle is moving, but it is going to stand still in a little while. That means that it must be slowing down at ...Note that the value a is directly related to the second derivative, since f ''(x) = 2a.. Definition. Let f(x) be a differentiable function on an interval I. (i) We will say that the graph of f(x) is concave up on I iff f '(x) is increasing on I. (ii) We will say that the graph of f(x) is concave down on I iff f '(x) is decreasing on I. Some authors use concave for concave down …Graphically, a function is concave up if its graph is curved with the opening upward (Figure 1a). Similarly, a function is concave down if its graph opens downward (Figure 1b). Figure 1. This figure shows the concavity of a function at several points. Notice that a function can be concave up regardless of whether it is increasing or decreasing.Question: 0 (b) Calculate the second derivative of f. Find where fis concave up, concave down, and has inflection points f"(x) = mining (36 06 Concave up on the interval Concave down on the interval Inflection points= (c) Find any horizontal and vertical asymptotes of f Horizontal asymptotes - Vertical asymptotes (d) The function is? because ? for all in the domainHere's the best way to solve it. 1) The funct …. Consider the following graph. Step 1 of 2: Determine the intervals on which the function is concave upward and concave downward. Enable Zoom/Pan 75 < 10 rev -75 Answer 4 Points Separate multiple entries with a comma -23 Answer 4 Points 3 me keypad Keyboard Shortcuts ev Separate multiple ...Step 2: Take the derivative of f ′ ( x) to get f ″ ( x). Step 3: Find the x values where f ″ ( x) = 0 or where f ″ ( x) is undefined. We will refer to these x values as our provisional inflection points ( c ). Step 4: Verify that the function f ( x) exists at each c value found in Step 3.Recall that the first derivative of the curve C can be calculated by dy dx = dy/dt dx/dt. If we take the second derivative of C, then we can now calculate intervals where C is concave up or concave down. (1) d2y dx2 = d dx(dy dx) = d dt(dy dx) dx dt. Now let's look at some examples of calculating the second derivative of parametric curves.1) Determine the | Chegg.com. Consider the following graph. 1) Determine the intervals on which the function is concave upward and concave downward. 2) Determine the x-coordinates of any inflection point (s) in the graph. Concave up: (-1,3); Concave down: (-0, -6) point (s): X=-1, x=3 (-6, -1) (3, 0); x-value (s) of inflection Concave up: (-6 ...1 Sections 4.1 & 4.2: Using the Derivative to Analyze Functions • f '(x) indicates if the function is: Increasing or Decreasing on certain intervals. Critical Point c is where f '(c) = 0 (tangent line is horizontal), or f '(c) = undefined (tangent line is vertical) • f ''(x) indicates if the function is concave up or down on certain intervals.Calculus. Find the Concavity f (x)=x^4-6x^2. f (x) = x4 − 6x2 f ( x) = x 4 - 6 x 2. Find the x x values where the second derivative is equal to 0 0. Tap for more steps... x = 1,−1 x = 1, - 1. The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the ... Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Concavity | Desmos Using the second derivative test, f(x) is concave up when x<-1/2 and concave down when x> -1/2. Concavity has to do with the second derivative of a function. A function is concave up for the intervals where d^2/dx^2f(x)>0. A function is concave down for the intervals where d^2/dx^2f(x)<0. First, let's solve for the second derivative of the function.Oct 19, 2021 ... Therefore, the function f is concave up on the interval (0, ∞). b. The function f has negative concavity where the second derivative is less ...Use a number line to test the sign of the second derivative at various intervals. A positive f " ( x) indicates the function is concave up; the graph lies above any drawn tangent lines, and the slope of these lines increases with successive increments. A negative f " ( x) tells me the function is concave down; in this case, the curve lies ...Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.Transcript. Inflection points are points where the function changes concavity, i.e. from being "concave up" to being "concave down" or vice versa. They can be found by considering where the second derivative changes signs. In similar to critical points in the first derivative, inflection points will occur when the second derivative is either ...Inflection points are found in a way similar to how we find extremum points. However, instead of looking for points where the derivative changes its sign, we are looking for points where the second derivative changes its sign. Let's find, for example, the inflection points of f ( x) = 1 2 x 4 + x 3 − 6 x 2 . The second derivative of f is f ...Determine the intervals on which the function is concave up or down and find the points of inflection. f (x) = 6 x 3 − 5 x 2 + 6 (Give your answer as a comma-separated list of points in the form (* ∗).Express numbers in exact form. Use symbolic notation and fractions where needed.) points of inflection: Determine the interval on which f is concave up. (Give your answer as an interval in ...Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.The graph of f f (blue) and f ′′ f ″ (red) are shown below. It can easily be seen that whenever f ′′ f ″ is negative (its graph is below the x-axis), the graph of f f is concave down and whenever f ′′ f ″ is positive (its graph is above the x-axis) the graph of f f is concave up. Point (0,0) ( 0, 0) is a point of inflection ...For the following function determine: a. intervals where f f f is increasing or decreasing b. local minima and maxima of f f f c. intervals where f f f is concave up and concave down, and d. the inflection points of f f f. f (x) = x 4 − 6 x 3 f(x)=x^{4}-6 x^{3} f (x) = x 4 − 6 x 3Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this siteDetermine the intervals on which the function is concave up or down and find the points of inflection. y=(x-2)(1-x^3) 4. 🤔 Not the exact question I'm looking for? Go search my question ... Calculate the power: y = - 2 Find the domain of the function without any restriction: x ...If the second derivative is positive on a given interval, then the function will be concave up on the same interval. Likewise, if the second derivative is negative on a given interval, the function will be concave down on said interval. So, calculate the first derivative first - use the power rule. #d/dx(f(x)) = d/dx(2x^3 - 3x^2 - 36x-7)#The inflection points of a function are the points where the function changes from either "concave up to concave down" or "concave down to concave up". To find the critical points of a cubic function f(x) = ax 3 + bx 2 + cx + d, we set the second derivative to zero and solve. i.e., f''(x) = 0. 6ax + 2b = 0. 6ax = -2b. x = -b/3aExcel is a powerful tool that offers a wide range of functions and formulas to help users perform complex calculations, analyze data, and automate tasks. However, with so many opti...Inflection points are points where the function changes concavity, i.e. from being "concave up" to being "concave down" or vice versa. They can be found by considering where the second derivative changes signs. In similar to critical points in the first derivative, inflection points will occur when the second derivative is either zero or ...So, for example, let f ( x) = x 4 − 4 x 3 and follow the steps to see where the function is concave up or concave down: Step 1: Find the second derivative. f ′ ( x) = 4 x 3 − 12 x 2. f ...A point where a function changes from concave up to concave down or vice versa is called an inflection point. Example 1: Describe the Concavity. An object is ...This is my code and I want to find the change points of my sign curve, that is all and I want to put points on the graph where it is concave up and concave down. (2 different shapes for concave up and down would be preferred. I just have a simple sine curve with 3 periods and here is the code below. I have found the first and second derivatives.The inflection points of a function are the points where the function changes from either "concave up to concave down" or "concave down to concave up". To find the critical points of a cubic function f(x) = ax 3 + bx 2 + cx + d, we set the second derivative to zero and solve. i.e., f''(x) = 0. 6ax + 2b = 0. 6ax = -2b. x = -b/3aJun 15, 2014 at 13:40. 2. It depends on your definition of concave: there are the notion of "concave" and "strictly concave". In x ≥ 0 x ≥ 0 arctan(x) arctan. ⁡. ( x) is concave, but not strictly concave. (The difference between the two notions translate in terms of the second derivative as the two conditions f′′ ≤ 0 f ″ ≤ 0 or ...Possible Answers: Correct answer: Explanation: The intervals where a function is concave up or down is found by taking second derivative of the function. Use the power rule which states: Now, set equal to to find the point (s) of infleciton. In this case, . To find the concave up region, find where is positive.A graph is generally concave down near a minimum and concave up near a maximum. Knowing where a graph is concave down and where it is concave up further helps us to sketch a graph. Theorem 3 (Concavity). If f00(x) >0 for all xin some interval, then the graph of f is concave up on that interval.The inflection points of a function are the points where the function changes from either "concave up to concave down" or "concave down to concave up". To find the critical points of a cubic function f(x) = ax 3 + bx 2 + cx + d, we set the second derivative to zero and solve. i.e., f''(x) = 0. 6ax + 2b = 0. 6ax = -2b. x = -b/3aOct 12, 2023 ... How do you find where the second derivative is concave up or concave down when given the graph of f(x)? ... Think of f'(x) as the function the “ ...Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-step0:00 find the interval that f is increasing or decreasing4:56 find the local minimum and local maximum of f7:37 concavities and points of inflectioncalculus ...Given a function f, use the first and second derivatives to find:1. The critical numbers2. The intervals over which f is increasing or decreasing3. Any local...Step 5 - Determine the intervals of convexity and concavity. According to the theorem, if f '' (x) >0, then the function is convex and when it is less than 0, then the function is concave. After substitution, we can conclude that the function is concave at the intervals and because f '' (x) is negative. Similarly, at the interval (-2, 2) the ...$\begingroup$ you look at the first derivative for the quasi properties it could tell you if its monotone F'(x)>=0 or F'(x)>0 , F'(x)>=0or and F injective, which is more that sufficient for all six (strict, semi-strict, standard quasi convexity and the other three for quasi concavity) quasi's if F'(x)>0 its also strictly pseudo linear and thus strictly pseudo linear, which are just those ...f (x)=3 (x)^ (1/2)e^-x 1.Find the interval on which f is increasing 2.Find the interval on which f is decreasing 3.Find the local maximum value of f 4.Find the inflection point 5.Find the interval on which f is concave up 6.Find the interval on which f is concave down. Anyone can explain? I know the f' (x)=e^-x (3-6x)/2 (x)^ (1/2) calculus. Share.Jul 12, 2022 · Estimate from the graph shown the intervals on which the function is concave down and concave up. On the far left, the graph is decreasing but concave up, since it is bending upwards. It begins increasing at $x = -2$, but it continues to bend upwards until about $x = -1$. we can therefore determine that: (1) By solving the equation: f '(x) = 0 ⇒ −2xe−x2 = 0. we can see that f (x) has a single critical point for x = 0, this point is a relative maximum since f ''(0) = −2 < 0. Looking at the second derivative, we can see that 2e−x2 is always positive and non null, so that inflection points and concavity ... Concavity relates to the rate of change of a function's derivative. A function f is concave up (or upwards) where the derivative f ′ is increasing. This is equivalent to the derivative of f ′ , which is f ″ , being positive. Similarly, f is concave down (or downwards) where the derivative f ′ is decreasing (or equivalently, f ″ is ... Take a "test number" from each interval and plug it into your function, in this case $-\cos x - \sin x$, and see if you you get a positive or negative number. The sign at the test point is the sign of the function on the entire interval. Here, your function is $2\pi$-periodic, so you only need to determine how the sign behaves over one period.The second partial derivative test tells us how to verify whether this stable point is a local maximum, local minimum, or a saddle point. Specifically, you start by computing this quantity: H = f x x ( x 0, y 0) f y y ( x 0, y 0) − f x y ( x 0, y 0) 2. Then the second partial derivative test goes as follows: If H < 0. ‍.Details. To visualize the idea of concavity using the first derivative, consider the tangent line at a point. Recall that the slope of the tangent line is precisely the derivative. As you move along an interval, if the slope of the line is increasing, then is increasing and so the function is concave up. Similarly, if the slope of the line is ...3. If the second derivative f'' is positive (+) , then the function f is concave up () . 4. If the second derivative f'' is negative (-) , then the function f is concave down () . 5. The point x=a determines a relative maximum for function f if f is continuous at x=a, and the first derivative f' is positive (+) for x<a and negative (-) for x>a.The sum of two concave functions is itself concave and so is the pointwise minimum of two concave functions, i.e. the set of concave functions on a given domain form a semifield. Near a strict local maximum in the interior of the domain of a function, the function must be concave; as a partial converse, if the derivative of a strictly concave ...The major difference between concave and convex lenses lies in the fact that concave lenses are thicker at the edges and convex lenses are thicker in the middle. These distinctions...Inflection Points. Added Aug 12, 2011 by ccruz19 in Mathematics. Determines the inflection points of a given equation. Send feedback | Visit Wolfram|Alpha. Get the free "Inflection Points" widget for your website, blog, Wordpress, Blogger, or iGoogle.Apr 24, 2022 · Similarly, a function is concave down if its graph opens downward (Figure $\PageIndex{1b}$). Figure $\PageIndex{1}$ This figure shows the concavity of a function at several points. Notice that a function can be concave up regardless of whether it is increasing or decreasing. The concavity of the function changes from concave up to concave down at 𝑥 = − 2 3. This is a point of inflection but not a critical point. We will now look at an example of how to calculate the intervals over which a polynomial function is concave up or concave down.An inflection point is a point on a function where the curvature of the function changes sign. ... Use Wolfram|Alpha to explore how the concavity of functions ...We say this function f f is concave up. Figure 4.34(b) shows a function f f that curves downward. As x x increases, the slope of the tangent line decreases. Since the derivative decreases as x x increases, f ′ f ′ is a decreasing function. We say this function f f is concave down.1. When asked to find the interval on which the following curve is concave upward. y =∫x 0 1 94 + t +t2 dt y = ∫ 0 x 1 94 + t + t 2 d t. What is basically being asked to be done here? Evaluate the integral between [0, x] [ 0, x] for some function and then differentiate twice to find the concavity of the resulting function? calculus.For $$$ x\gt0 $$$, $$$ f^{\prime\prime}(x)=6x\gt0 $$$ and the curve is concave up. This confirms that $$$ x=0 $$$ is an inflection point where the concavity changes from down to up. Concavity. Concavity describes the shape of the curve of a function and how it bends. The curve can be concave up (convex down), concave down (convex up), or neither.f (x)=3 (x)^ (1/2)e^-x 1.Find the interval on which f is increasing 2.Find the interval on which f is decreasing 3.Find the local maximum value of f 4.Find the inflection point 5.Find the interval on which f is concave up 6.Find the interval on which f is concave down. Anyone can explain? I know the f' (x)=e^-x (3-6x)/2 (x)^ (1/2) calculus. Share.Free online graphing calculator - graph functions, conics, and inequalities interactivelySo, since an increasing first derivative indicates concave up, a positive second derivative indicates concave up. Similarly, as a decreasing first derivative indicates concave down, a negative second derivative indicates concave down. The point where the function switches concavity is called the inflection point. Because the function's first ...Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.Now that we know the second derivative, we can calculate the points of inflection to determine the intervals for concavity: f ''(x) = 0 = 6 −2x. 2x = 6. x = 3. We only have one inflection point, so we just need to determine if the function is concave up or down on either side of the function: f ''(2) = 6 −2(2)Now that we know the second derivative, we can calculate the points of inflection to determine the intervals for concavity: f ''(x) = 0 = 6 −2x. 2x = 6. x = 3. We only have one inflection point, so we just need to determine if the function is concave up or down on either side of the function: f ''(2) = 6 −2(2)Determine where the function is increasing, decreasing, concave up, concave down. Sketch the graph of each function and label the intervals where it is increasing, decreasing, concave up, concave down. y= -2/ (x 2 +3) Here's the best way to solve it.Teen Brain Functions and Behavior - Teen brain functions aren't like those of adults. Why do teens engage in risk-taking behaviors? Because the teen brain functions in a whole diff...The concavity of the graph of a function refers to the curvature of the graph over an interval; this curvature is described as being concave up or concave down. Generally, a concave up curve has a shape resembling "∪" and a concave down curve has a shape resembling "∩" as shown in the figure below. Concave up.With just a few clicks, users can access a wide range of online calculators that can perform calculations in a variety of fields, including finance, physics, chemistry, and engineering. These calculators are often designed with user-friendly interfaces that are easy to use and provide clear and concise results. Concave Up Or Down Calculator.f (x)=3 (x)^ (1/2)e^-x 1.Find the interval on which f is increasing 2.Find the interval on which f is decreasing 3.Find the local maximum value of f 4.Find the inflection point 5.Find the interval on which f is concave up 6.Find the interval on which f is concave down. Anyone can explain? I know the f' (x)=e^-x (3-6x)/2 (x)^ (1/2) calculus. Share.Graphically, a function is concave up if its graph is curved with the opening upward (Figure 1a). Similarly, a function is concave down if its graph opens downward (Figure 1b). Figure 1. This figure shows the concavity of a function at several points. Notice that a function can be concave up regardless of whether it is increasing or decreasing.Find the local maximum value(s). (Enter your answers as a comma-separated list.) (c) Find the inflection points. smaller x-value (x, y) = larger x-value (x, y) = Find the interval(s) where the function is concave up. (Enter your answer using interval notation.) Find the interval(s) where the function is concave down.Nov 18, 2022 · Intuitively, the Concavity of the function means the direction in which the function opens, concavity describes the state or the quality of a Concave function. For example, if the function opens upwards it is called concave up and if it opens downwards it is called concave down. The figure below shows two functions which are concave upwards and ... Step 5 - Determine the intervals of convexity and concavity. According to the theorem, if f '' (x) >0, then the function is convex and when it is less than 0, then the function is concave. After substitution, we can conclude that the function is concave at the intervals and because f '' (x) is negative. Similarly, at the interval (-2, 2) the ...

An inflection point is defined as a point on the curve in which the concavity changes. (i.e) sign of the curvature changes. We know that if f ” > 0, then the function is concave up and if f ” < 0, then the function is concave down. If the function changes from positive to negative, or from negative to positive, at a specific point x = c .... However to a texter

Possible Answers: Correct answer: Explanation: The intervals where a function is concave up or down is found by taking second derivative of the function. Use the power rule which states: Now, set equal to to find the point (s) of infleciton. In this case, . To find the concave up region, find where is positive.This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: Determine the intervals on which the given function is concave up or down and find the points of inflection. Letf (x)= (x^2-6)e^xInflection Point (s) = ____The left-most interval is ___ and on this interval f ...minimum in the calculate menu since the parabola is concave up. If it were concave down, you would need to key in "4" (maximum) in the calculate menu. If you have a TI-86, use the following key strokes: Note 1: The direction of the first arrow (right) in the instructions above assumes your cursor is to the leftThis problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: Determine the intervals on which the given function is concave up or down and find the points of inflection. Letf (x)= (x^2-6)e^xInflection Point (s) = ____The left-most interval is ___ and on this interval f ...Estimate from the graph shown the intervals on which the function is concave down and concave up. On the far left, the graph is decreasing but concave up, since it is bending upwards. It begins increasing at $x = -2$, but it continues to bend upwards until about $x = -1$.What x values is the function concave down if #f(x) = 15x^(2/3) + 5x#? ... On what intervals the following equation is concave up, concave down and where it's inflection... See all questions in Analyzing Concavity of a Function Impact of this question. 7581 views around the world ...Sep 18, 2020 · Wolfram Language function: Compute the regions on which an expression is concave up or down. Complete documentation and usage examples. Download an example notebook or open in the cloud. Here's the best way to solve it. 1. You are given a function f (x) whose domain is all real numbers. Describe in a short paragraph how you could sketch the graph without a calculator. Include how to find intervals where f is increasing or decreasing, how to find intervals where f is concave up or down, and how to find local extrema and points ...f (x)=3 (x)^ (1/2)e^-x 1.Find the interval on which f is increasing 2.Find the interval on which f is decreasing 3.Find the local maximum value of f 4.Find the inflection point 5.Find the interval on which f is concave up 6.Find the interval on which f is concave down. Anyone can explain? I know the f' (x)=e^-x (3-6x)/2 (x)^ (1/2) calculus. Share.f (x) = x³ is increasing on (-∞,∞). A function f (x) increases on an interval I if f (b) ≥ f (a) for all b > a, where a,b in I. If f (b) > f (a) for all b>a, the function is said to be strictly increasing. x³ is not strictly increasing, but it does meet the criteria for an increasing function throughout it's domain = ℝ.Similarly, a function is concave down if its graph opens downward (Figure $\PageIndex{1b}$). Figure $\PageIndex{1}$ This figure shows the concavity of a function at several points. Notice that a function can be concave up regardless of whether it is increasing or decreasing.Given the functions shown below, find the open intervals where each function’s curve is concaving upward or downward. a. f ( x) = x x + 1. b. g ( x) = x x 2 − 1. c. h ( x) = 4 x 2 – 1 x. 3. Given f ( x) = 2 x 4 – 4 x 3, find its points of inflection. Discuss the concavity of the function’s graph as well..

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