(x +3)³4(x – 1)2121611Consider the function f(x)Note that441(x – 1)2-|(x – 9)(x + 3)²4(x – 1)324(x + 3)f'(x) =and f"(x) =(r – 1)4Use the Mean Value Theorem to show that the equation f' (x) = 0.01 has a solution in the interval(-4,-3).

Answered: (x +3)³ 4(x – 1)2 12 16 11 Consider the…

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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2 If f(x) = (x³ + 3x)*, what is f'(x)? O f'(æ) = (x³ +3æ) O f'(x) = (x³ + 3x) (3x² +3) O f'(x) = 2 (2³ + 3æ) (3x² + 3) O f'(æ) = 2 (x³ + 3x)
If h(x) = f(g(x)) and you have following information about f(x) and g(x): 1 2 3 4 f(x) f'(x) g(x) 4 1 3 2 1 3 4 3 2 1 4 (x),6 3 4 1 then h'(3) :
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(x +3)3 4(x – 1)² 12 + 4 16 11 Note that 4 Consider the function f(x) 1 (x – 1)2 (a – 9)(x + 3)² 4(x – 1)3 24(x + 3) f' (x) = and f"(x) = (x – 1)4 * Construct a table of signs for f' and f" which specifies the following: a) The intervals on which the graph of fis inereasing, decreasing, concave up, and concave down and b) The values of x at which fhas relative extrema, inflection points, and vertical asymptotes (if any).
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3 1. Find the local extremes of f (x) = x³ +2xª using the first derivative test.
Determine the local optima of the following functions using both the First derivative test and Second derivative test.
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2. Using the information in the table about f and g, find: (a) h(4) if h(x) = f(g(x)) (b) h '(4) if h(x) = f(g(x))(Hint: use chain rule) (c) h(4) if h(x) = g(f(x)) (d) h '(4) if h(x) = g(f(x)) (Hint: use chain rule) (e) h '(4) if h(x) = g(x)/f(x) (f) h '(4) if h(x) = f(x)g(x) Please show your work X 1 4 f(x) f'(x) 3 2 1 4 1 4 2 g(x) 2 1 4 3 g '(x) 4 2 3 1 3. 3.

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(x +3)³ 4(x – 1)2 12 16 11 Consider the function f(x) Note that 4 4 1 (x – 1)2 - | (x – 9)(x + 3)² 4(x – 1)3 24(x + 3) f'(x) = and f"(x) = (r – 1)4 Use the Mean Value Theorem to show that the equation f' (x) = 0.01 has a solution in the interval (-4,-3).