4 Graph of f The figure above shows the graph of f on the interval (0, 4]. Which of the following could be the graph of f', the derivative of f, on the interval (0, 4] ? A

Q: Find all relative extrema of the function. Use the second derivative test to determine the extrema.…

A: We will find the relative extrema and the value of f"(2) as following. The function given f(x)=x^2…

Q: 3. The second derivative of the function is given by: [K: 2] a) Determine the interval where the…

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Q: Graphs of functions are shown in [-5, 5, 1] by [-5, 5, 1] viewing rectangles. Match the function…

A: Given: Graphs of functions are shown in [-5, 5, 1] by [-5, 5, 1] viewing rectangles. To Match: the…

Q: Finding and Evaluating a Derivative InExercises 17–24, find f x and f c. 21. f (x) = x cos x,…

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Q: Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

A: Use derivative and critical point for finding the absolute maxima .

Q: The first derivative of f(x) is f’(x)= -3(x-1)/(x+7)^3 Find the intervals where f(x) is increasing.

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Q: 14. Consider the function f(x) = xª – 2x?. %3D - a) Find the interval(s) where the function is…

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Q: Even and Odd Functions:-    Show that the derivative of an odd function is even. That is, if f ( -x)…

A: Query-  Show that the derivative of an odd function is even. That is, if f ( -x) = -f (x), then f'…

Q: f(g(x)) = (3x² f (g(x)) = (x)(x² +3)² (За* — 2х + 4)°

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Q: 2) The graph of a function y = f(x) is given. Draw a graph of it's derivative %3D

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Q: The second derivative of the function fis given by f" (z) = At what values of z in the interval (-4,…

A: topic - application of derivatives

Q: Assume that functions f and g are differentiable with f(-5)% = -4, f'(-5) = -4, g(-5)= -3, and…

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Q: Determine the derivative of f(x) = -

A: To determine the derivative of fx=x3ex. Solution: Quotient rule of differentiation states that:…

Q: 3. Find the r-value for all relative extrema of f(x) using the first derivative test. 1 + 3 1 f(x):…

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Q: estion: Find the derivative of the following 1. function: y = In vtan x

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Q: Vertical tangent lines If a function ƒ is continuous at a andlimx-a 0 ƒ′(x) 0 = ∞, then the curve y…

A: Consider the given function: Here the objective is to verify that f(x) has a vertical tangent line…

Q: Right- and left-hand derivatives Let f (x) = |x|. (a) Calculate the right-hand derivatives of f(x)…

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Q: Find the Derivative of a Square Find the derivative of f2(x) working from the definition f'(x) : f(x…

A: Given: The derivative of the function fx is f'x=limh→0fx+h-fxh To determine: The derivative of f2x…

Q: 1)Describe the purpose of finding the first and second derivatives to sketch a graph of functions.

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Q: Using trignometric finction/s:-   Find the derivative of the function g(x) = sin2 x + cos2 +x in two…

A: To find the derivative of the function: g(x)=sin2x+cos2x+x Solution: g(x)=sin2x+cos2x+x ⇒g(x)=1+x…

Q: a. Find the local extrema of each function on the given interval,and say where they occur.b. Graph…

A: Given  The function is fx=x2-2sinx2  ,0≤x≤2π.

Q: 5. The graph of f', the derivative of f, is shown below. Find the x-values of all relative extrema.…

A: Apply second derivative test

Q: The derivative of sin 2x Graph the function y = 2cos 2x for -2 < x< 3.5. Then, on the same screen,…

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Q: 3. Definition of the Derivative. Use the definition of the derivative to find the derivatives of the…

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Q: 3. 1 Graph of f" The graph of f", the second derivative of the function f, is shown above. Which of…

A: The graph of f" seems to be the graph of x2-1.5 Although f"(x), can be integrated two times to get…

Q: th Determine an expression for f(") (x) (the n' derivative of f) if f (x) = x¯' (Hint: take a few…

A: Let's find.

Q: Describe the purpose of finding the first and second derivatives to sketch a graph of functions.

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: - 6x + 2 on the domain [-7,2]. Find the absolute extrema if they exist, as well as all values of x…

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Q: Let f(x) = 3x2 - 2x. (a) Use the definition of derivative and the Procedure/Example box in this…

A: We have to find derivative

Q: quotient rule f(x) - in terms of f and g? g(x) What is the derivative of ? - 3 – 1 -cos(t) Compute…

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Q: 27. The Graph of the Derivative Function Given the graph of f(x) below, what is the open interval(s)…

A: f'(x) will be positive if f(x) is increasing.

Q: Graph of f' The graph of f, the derivative of the function f, is shown above for 0 < I < 9. Which of…

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Q: Find the derivative of  f(z)=−5⋅2z.   Enclose arguments of functions, numerators, and denominators…

A: We differentiate both sides with respect to z

Q: Higher-order derivatives Find ƒ′(x), ƒ″(x), and ƒ‴(x) for thefollowing functions. ƒ(x) = 10ex

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Q: 18 + X Find the absolute extrema of the function f(x) = on the interval [6,9]. 18 - x Find the…

A: We absolute exterma and second derivatives.

Q: Quotient Rule for the second derivative Assuming the firstand second derivatives of f and g exist at…

A: To Determine: find a formula for d2dx2f(x)g(x) Given: the first and second derivatives of f and g…

Q: Q: 1 the first derivative test to find the intervals on which the function f(x) = xe-* = is…

A: Given, f(x)=xe-x

Q: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting…

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Q: Higher-order derivatives Find ƒ′(x), ƒ″(x), and ƒ‴(x).

A: Given, f(x)=x2(2+x-3)

Q: Consider the function: f(x) = x² – 4x + 9 Step 2 of 2: Use the First Derivative Test to classify the…

A: Given function is fx=x2−4x+9 Differentiate fx=x2−4x+9 with respect to x, we get f'x=2x−4 Now, for…

Q: 2. The graph of the derivative function f'(x) of a function f(x) a) Determine: the intervals where…

A: f(x) will be increasing in the range where f'(x) is positive.f(x) is increasing in the range (-∞, 1)…

Q: 65. f(x) 3 х2 — 5, с %3D 3

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Q: 2. If a function f(x) is differentiable at x-a, then function f(x) is continuous at? А. х-а В. х-х…

A: Given problems:-

Q: 2. Given f (x) = x-(4 – x) a. Show work for finding derivative. Simplify derivative. b. Find…

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Q: Find the local maximum and minimum values of the function f (x) = -I - using the Second Derivative…

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Q: 3. What is the derivative of y evaluate the derivative at x = 0, and you are given that g(0) f(1) =…

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Q: = 0 and f " (5) = – 1. Suppose that for a certain function ƒ ’ (5) Then, using the Second Test, f(5)…

A: We have, f'5 = 0 f''5 = -1

Q: A function  f(x) has a relative extremum at x=π. If the second derivative of the function is…

A: Given              A function  f(x) has a relative extremum at x=π. If the second derivative of the…

Q: f(x) = 3-* cos (x²)

A: We need to find the derivative of the function. f(x)=3-xcosx2  Now,         f'(x)=3-xcosx2' Apply…

Q: 75. Derivatives from tangent lines Suppose the line tangent to the graph of f at x = 2 is y = 4x + 1…

A: The line tangent to the graph of f at x=2 is y=4x+1.