Consider the following. (If an answer does not exist, enter DNE.) f'(x) = 4x2 – 1 (a) Find the open intervals on which f'(x) is increasing or decreasing. (Enter your answers using interval notation.) increasing (0, 0) decreasing (-∞, 0) (b) Find the open intervals on which the graph of f is concave upward or concave downward. (Enter your answers using interval notation.) concave upward (0, 0) (-∞, 0) concave downward (c) Find the x-values of the relative extrema of f. (Enter your answers as a comma-separated list.) relative maximum X = relative minimum X = Find the x-values of the inflection points of f. (Enter your answers as a comma-separated list.) X = 0

Q: Q2/ A/ Show that the functions f(x) = sin-1() and g(x) = 2tan-Vx, have the same derivative. %3D

A: Given : f(x)= sin-1 ( x-1 / x+1 ) g(x) = 2 tan-1 (√x)

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A: (a) f(x)=52x-3 f'(x)=limt→xf(t)-f(x)t-x        =limt→x52t-3-52x-3t-x…

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Q: 1. Find the derivative. g(x)=(4x-2)^5-√(x^2+8)

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

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A: Solved below

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A: Find the derivative

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A: We will find out the required function.

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Q: 9. Suppose for sume funchion f we have its derivative, f'x) = e*sin(x), on the %3D interval o< x<…

A: We can use application of derivative in order to solve the given problem.

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A: To find inflection points of the function we need second derivative of the function.Use product rule…

Q: 4. Find the first derivative of the given function using the Rules of Differentiation: a. h(x) = X-…

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Q: The derivative of f(x) with respect to x is the function f'(x) and is defined as f'(x) = lim 0…

A: To find f(x+h) replace x by x+h in f(x).

Q: 2. Let f(x) = /1 – x² . Find f(8) (0), i.e., the eighth derivative of ƒ evaluated at the point 0.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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A: Given thatf(x)=xln(x2-3)+5f'(x)=ddxxln(x2-3)+5         =xddxln(x2-3)+ln(x2-3)ddx(x)+ddx(5)…

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A: True or False The graph of y = cos x is decreasing on the interval (0, π).

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A: the function is decreasing when  as we can see from the graph,  on the interval  and  which means…

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A: we have to find the derivative using definition. as per definition  f'(x)=limh→0f(x+h)-f(x)h

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A: The given function is :f(x)=x55-x33 To find: Critical points of f, and  we need to classify them…

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

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A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 2. Determine the 8th derivative of y with respect to x of the function 1 f(x) = 1+x2 and find the…

A: Taylor series

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Q: 4. The derivative of f(x) = ln x at x = 3 when hpresent = 0.001 and hprevious = 0.002. %3D 5. The…

A: f(x)=ln…

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Q: 11 with respect to x is The derivative of y = cos - 1

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A: Given: gx=x2 sin1x,       if x≠00,     if x=0 To Find: Is g differentiable at x=0? If so, to find…