7: The graph of f' is given to the right. Which of the below graphs is a graph of its antiderivative f? (A) (B)

Q: Suppose that the differentiable function y = f(x) has an inverse, that the graph of f passes through…

A: first we find equation of line which passes through (2,5) and slope (m)=1/4 y-5=m(x-2)…

Q: The function f(x) = 3x³ + cos(3ræ) + 2x , x > 1 is known to be a strictly increasing function on its…

A: Given f(x) = 3x3 + cos(3πx) + 2x,  x≥1   ⇒ f'(x) = 9x2 - 3πsin(3πx) + 2

Q: Find all the antiderivatives of the following function. Check your work by taking derivatives. h(z)…

A: To find the antiderivative, we will integrate.  C=integrating constant

Q: 3 Given the function: f(x) = (1+ x)³/2 . x - 1 Prove that it is increasing on (0, +00) analytically,…

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Q: 1 What is the lineur is The slope of the line tangent to the graph y = cos x at the point x =…

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Q: 5) Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.…

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Q: 4. Suppose fand f'are differentiable functions of x. Given f' (4) = 0, f" (-), and g(x) = (). log…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: shows the graphs of the first and second derivatives of a function y = ƒ(x). Copy the picture and…

A: The graph of y=f"(x) is a linear function. So it is of degree 1.  The graph of y=f'(x) is a…

Q: 1) Find the derivative of the function g(x) = (arctan x)3, first showing how to get the d formula…

A: As per guideline we have solve only one question

Q: 4. The graph of f' (x), the derivative of f of x, is continuous for all x and consists of five line…

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Q: 2. Find all x values on the graph of f (x) where the tangent line is horizontal for each of the…

A: To find: The values of x on the graph f(x) where the tangent line is horizontal. Given information:…

Q: The limit cos(x) +1 lim x – 9T represents the derivative of some function f(x) at some number a.…

A: In the given question, f(x) is cos(x) and a is 9π

Q: 8. Given that f(r) is continuous at r = 0, is f(r) differentiable at z = 0? (If yes, find f(0) using…

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Q: (b) Sketch the graph of f (x) = ln(4 – x²). Use the first and second derivatives to identify where…

A: Consider the function  fx=ln4−x2

Q: 2. Find a function of the form y = Asin(x) + D or y = Acos(x) +D whose graph matches the graph…

A: We know that time period of sin(x) and cos(x) both are 2π

Q: Q6. Find the first derivatives by using chain rule of the following functions: i. f(x) = tan %3D ii.…

A: Given that:                       (i) f(x)=tan1x(ii)g(x)=lnx3+x-1

Q: 5. Suppose there exits positive differentiable a(x) and B(x) such that a*(x) – B°(x) = 3, and a'(x)…

A: Given: α3x - β3x = 3                                                    1       α'x          =5βx…

Q: 1. Below is the graph of f(x) = |x]. Using the left side of the function with the equation y = – x,…

A: The graph of fx=x is given. The equation for the left side of the graph is y=-x and the equation…

Q: 3. The slope of the tangent line to f(x) = A tan(¤) is 1/2 when z = 2n/3. Deter- mine the equation…

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Q: Use the Chain Rule to find the derivative. y = cos (e40) (Express numbers in exact form. Use…

A: Given.

Q: 3. Below is the graph of a function f(x) on the interval [0, 6]. Sketch the graph of its derivative…

A: Given the graph of f(x) on the interval [0, 6] To obtain is graph of f'(x)  on the same interval [0,…

Q: 1. Find the derivative of the following functions. (find y') a. у %3DIn(cos(20)) b. cos(xy) = x - y…

A: Since you have posted a question with multiple subparts, we will solve first three subparts for you.…

Q: Draw simple graphs of the first and second derivatives of the function y = f(x) whose graph is given…

A: Given,

Q: 4. For what values of x does the graph of f have a horizontal tangent if f(x) = V3 x – 2 sin(x).

A:

Q: The graph below is of f "(x) for some function f(x) with domain (-∞, ∞) (i.e., the graph of of the…

A: Since you have asked a question with multiple question in a single request, we would be answering…

Q: 1. Find the derivative of each of the following functions a) f(x) = cos5x %3D b) g(x) = cos 5x c)…

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Q: (1) For every natural number n, x" = nx"-1 (you may use the product rule for derivatives and that x…

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Q: 10. Consider the function f(x, y) = 4 + x* + 3y* a. Show that the Second Derivative Test is…

A: (a) Calculate the value for second partial derivatives w.r.t x and y.…

Q: The function defined by x2 if r 0 is continuous at a = 0. Determine the left- and right-hand…

A: We have to check our function is differentiable at x=0 or not

Q: Find all the antiderivatives of the following function. Check your work by taking derivatives. g(x)…

A: Given function is gx=11x10. Antiderivative is opposite of derivative. Antiderivative means…

Q: The first derivative of the function h is given by h'(x) = tan(0.1x- x) for -n < x < R. On what…

A: Solution Given h'(x)=tan(0.1x3-x) for -π&lt;x&lt;π.we need to find on what intervals is h…

Q: Which of the following is the graph of an antiderivative of f(x), shown below? f(x):

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Q: 2. Find the derivatives of the following functions. 4 a. f(x) = 3x³ x2 b. f(x) = (4 – x²)" C. f(x) =…

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Q: ose k is the derivative of K, a function with the same domain as k. inction K has one critical point…

A: According to answer policy we can answer one question at a time, therefore I will be answering first…

Q: The graph of derivation function g(x) for a differentiable function g(x) over R is given below and…

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Q: 4. Find the second-order derivative of the following function: f(z) = log, cos z + In %3D

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Q: ау 3 • Find for y = dx in each of the following ways: o Use the limit definition of the derivative;…

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Q: 3. Compute the following derivatives using the chain rule: [f(g(x))] = f'(g(x))g'(x). In each part,…

A: Given: a) ddxln(cosx)b) ddxxex

Q: Find all the antiderivatives of the following function. Check your work by taking derivatives. g(x)…

A: To find antiderivative of function gx=-4cosx-x. Solution: Antiderivative means integration. We have…

Q: 2. Consider the function below and the point (x, y, z) shaded in red. Is fa positive, negative, or…

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Q: Consider the derivative function g (x) = 3 cos (4x – 1). %3| What is the general antiderivative of…

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Q: Define h(x) = x° sin(1/x) for x # 0 and h(0) = 0. Prove that h is differentiable at x = 0, and find…

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Q: A. Give a piecewise-defined function f (x) with no extreme values. B. Find for x² – 4xy + y² = 7 by…

A: A). A piecewise function is: fx=2x≤1xx&gt;1 Graph for this piecewise function is: B. Given function…

Q: e) The function f(x) = log(x)log(x) with x %3D Jse fzero to find a zero of its derivative. What is…

A: The given function is f(x)=log(x)log(x); with x≥1

Q: 1) Suppose the second derivative of a contiovous function given by f"(x)=Cx-2 )3 (x-2)2 (sx-) A…

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Q: 10.The graph of f'(x), the derivative of f, is given below for -6 Sxs7.On what intervals is the…

A: Option (c) is correct Because f'(x) is greater or equal to zero in that interval. Or we can say…

Q: 7. Use the limit definition of the derivative to find f'(x). Then find the equation of the tangent…

A: