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3. Consider the following table of values for two functions f and g: X 1 2 3 4 f(x) 2 4 1 3 f'(x) -6-7-8 -9 g(x) g'(x) Table 1: Table of Values 2 27 3 3 7 4 1 4 5 7 7 Using this table, compute the following: (a) If h(x) = f(g(x)), find h'(1) Solution: Using the chain rule, we know that h'(x) = f'(g(x)) · g'(x). Therefore h'(1) = f'(g(1)) · g'(1) = f'(2) g'(1) = 2 = -7. = -2 7

3. Consider the following table of values for two functions f and g: X 1 2 3 4 f(x) 2 4 1 3 f'(x) -6-7-8 -9 g(x) g'(x) Table 1: Table of Values 2 27 3 3 7 4 1 4 5 7 7 Using this table, compute the following: (a) If h(x) = f(g(x)), find h'(1) Solution: Using the chain rule, we know that h'(x) = f'(g(x)) · g'(x). Therefore h'(1) = f'(g(1)) · g'(1) = f'(2) g'(1) = 2 = -7. = -2 7

Calculus: Early Transcendentals
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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3. Consider the following table of values for two functions f and g: X 1 2 3 4 f(x) 2 4 1 3 f'(x) - -7 -8 -9 3 4 1 g(x) 2 g'(x) 2 4 ²/3/5 7 7 7 Table 1: Table of Values Using this table, compute the following: (a) If h(x) = f(g(x)), find h'(1) Solution: Using the chain rule, we know that h'(x) = f'(g(x)) · g'(x). Therefore h'(1) = f'(g(1)) · g'(1) = f'(2) · g'(1) = −7. 2 -2 7 =
Transcribed Image Text:3. Consider the following table of values for two functions f and g: X 1 2 3 4 f(x) 2 4 1 3 f'(x) - -7 -8 -9 3 4 1 g(x) 2 g'(x) 2 4 ²/3/5 7 7 7 Table 1: Table of Values Using this table, compute the following: (a) If h(x) = f(g(x)), find h'(1) Solution: Using the chain rule, we know that h'(x) = f'(g(x)) · g'(x). Therefore h'(1) = f'(g(1)) · g'(1) = f'(2) · g'(1) = −7. 2 -2 7 =
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