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Question 4 If f and g are the functions whose graphs are shown, let h(a) =9(f(x)). Find h'(1). -2 oter your anoweras an lateger or aredueel fraction. Question 5

Question 4 If f and g are the functions whose graphs are shown, let h(a) =9(f(x)). Find h'(1). -2 oter your anoweras an lateger or aredueel fraction. Question 5

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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**Question 4** If \( f \) and \( g \) are the functions whose graphs are shown, let \( h(x) = g(f(x)) \). Find \( h'(1) \). **Graph Explanation** The image contains a graph with two plotted linear functions, \( f \) in red and \( g \) in blue, on a coordinate plane. The x-axis ranges from -2 to 6, and the y-axis ranges from 0 to 6. - The red line \( f \) starts at the point (-2, 0), moves up to (2, 4), and then goes down to (4, 0). - The blue line \( g \) begins at (-2, 6) and steadily decreases to (2, 2) and continues to increase back to (4, 6), and then extends beyond the visible grid. The graphs depict piecewise linear functions with different slopes in the segments. **Prompt** Enter your answer as an integer or a reduced fraction.
Transcribed Image Text:**Question 4** If \( f \) and \( g \) are the functions whose graphs are shown, let \( h(x) = g(f(x)) \). Find \( h'(1) \). **Graph Explanation** The image contains a graph with two plotted linear functions, \( f \) in red and \( g \) in blue, on a coordinate plane. The x-axis ranges from -2 to 6, and the y-axis ranges from 0 to 6. - The red line \( f \) starts at the point (-2, 0), moves up to (2, 4), and then goes down to (4, 0). - The blue line \( g \) begins at (-2, 6) and steadily decreases to (2, 2) and continues to increase back to (4, 6), and then extends beyond the visible grid. The graphs depict piecewise linear functions with different slopes in the segments. **Prompt** Enter your answer as an integer or a reduced fraction.
**Question 9** If \( h(x) = \sqrt{7f(x)} - 10 \), where \( f(1) = 2 \) and \( f'(1) = 8 \), find \( h'(1) \). Your answer should be an integer (like -2 or 3), a simplified proper fraction (like -3/2). --- **Question 10** Find the derivative of \( y = \cos^3(\sin x) \). - \( 3 \cos x \cos^2(\sin x) \) - \( 3 \cos x \cos^2(\sin x) \sin(\sin x) \) - \( 3 \cos x \cos^2(\sin x) \) - \( 3 \cos x \cos^2(\sin x) \sin(\text{derivative info}) \)
Transcribed Image Text:**Question 9** If \( h(x) = \sqrt{7f(x)} - 10 \), where \( f(1) = 2 \) and \( f'(1) = 8 \), find \( h'(1) \). Your answer should be an integer (like -2 or 3), a simplified proper fraction (like -3/2). --- **Question 10** Find the derivative of \( y = \cos^3(\sin x) \). - \( 3 \cos x \cos^2(\sin x) \) - \( 3 \cos x \cos^2(\sin x) \sin(\sin x) \) - \( 3 \cos x \cos^2(\sin x) \) - \( 3 \cos x \cos^2(\sin x) \sin(\text{derivative info}) \)
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