4.b.a.1. Selected values of f, g, and their derivatives are given in the table.f(x)-3-125811,X1041-2-55Let (x) = f(x)g(x).g(x)1-2-5Let h(x) = f(x) · g(x). Find h'(11).h(x) =Find j'(-3).-3118f'(x)-1-3O2713g'(x)3O-28-3.51

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Answered: 4. b. a. 1. Selected values of f, g,…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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8,9 need both
Consider the following. 2x f(x) x + 2 Use a computer algebra system to find the derivative of the function. Then use the utility to graph the function and its derivative on the same set of coordinate axes. O y y 2- 0 --2 0 -1- 1 1 2 f(x) f(x) 2 3 3 X 4 O f' is never zero. O f approaches √2 when f' is zero. Of approaches -√2 when f' is zero. 4 5 f'(x) f'(x) 5 0 -1- Describe the behavior of the function when the derivative is zero. Of approaches to when f' is zero. O 3¹¹f'(x) 0.5 3 f'(x) 0 0.5 1 to X 2 1.5 2 X 2.5 f(x) f(x) 2.5 3
excluding question 1
I need answer 2,3
3. Consider the function p(x) = (2x³ − 4x +3) 6. A. If ƒ(x) = 2x³ — 4x + 3 and g(x) = x6, then function p is equal to exactly one of the following: f og or go f. Which is it? Explain. B. Thinking of function p as the appropriate composition of functions from Part A, apply the chain rule for derivatives to compute an expression for p'(x). C. Using the chain rule for the derivative computation in Part B is much more efficient than distributing out the product of the six polynomials multiplied in the original expression of f, simplifying that result, and then computing the derivative of that simplified result using the technique from Exercise 1A. Explain. (Please do not waste your time performing this beastly computation, just explain why it would be much more computationally intensive than what was done in Part B.
15. Let a be a real number. We will explore the derivatives of the function f(x) = eax. By using the chain rule, we see (a) What is Recall that the second derivative of a function is the derivative of the deriva- tive function. Similarly, the third derivative is the derivative of the second derivative. (b) What is d² dx² d3 C030 BY NO SA d dx = aeax (eax), the third derivative of eax? (c) Let n be a natural number. Make a conjecture about the nth derivative dn of the function f (x) = eax. That is, what is (eax)? This con- dxn jecture should be written as a self-contained proposition including an appropriate quantifier. (eax), the second derivative of eax? 4.1. The Principle of Mathematical Induction (d) Use mathematical induction to prove your conjecture. 183
Find the derivative of each of the functions below. SIMPLIFY your answers. 40 39) f(x) = (5x − 8)4 40) g(x) = tan(x² −9) 42) f(x) = 5 (x = 1)* x+1 41) h(x)=√10-x³ 43) f(x) = cot(cos.x) 44) f(x) = cot³ x of people that are playing a new game t weeks after it is introduced is given
1. The figure below shows the graph of f', the derivative of the function f, on the closed interval from x = -2 to x = 6. The graph of the derivative has horizontal tangent lines at x = 2 and x = 4. (6,4) W (2₂0) (5,0) (3,-1) (0, -2) (4,-2.5) All (-2,-3) Find the x-value where f attains its absolute maximum value on the closed interval from x = -2 to x = 6. Justify your answer

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4. b. a. 1. Selected values of f, g, and their derivatives are given in the table. f(x) 10 4 1 -2 -5 5 -3 2 5 8 11, x Let h(x) = f(x) · g(x). Find h'(11). h00= Let (x) = f(x) g(x) g(x) 1 -2 -5 -3 11 8 Find j'(-3). f'(x) -1 -3 2 7 13 g'(x) 3 0 -2 8 -3.5 1