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f(3) = 5, g(3) = -4, f'(3) = -2, g'(3) = 7, f'(5) = 3, g'(5) = 10 a) If h(x) = f(x)g(x), find h'(3). b) If h(x) = f(x) find h'(3). g(x)+1' c) If h(x) = g(f(x)), find h'(3).

f(3) = 5, g(3) = -4, f'(3) = -2, g'(3) = 7, f'(5) = 3, g'(5) = 10 a) If h(x) = f(x)g(x), find h'(3). b) If h(x) = f(x) find h'(3). g(x)+1' c) If h(x) = g(f(x)), find h'(3).

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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The image presents a set of calculus problems involving derivatives with given functions and their values at specific points. **Given Information:** - \( f(3) = 5 \) - \( g(3) = -4 \) - \( f'(3) = -2 \) - \( g'(3) = 7 \) - \( f'(5) = 3 \) - \( g'(5) = 10 \) **Problems:** a) **If \( h(x) = f(x)g(x) \), find \( h'(3) \).** b) **If \( h(x) = \frac{f(x)}{g(x)+1} \), find \( h'(3) \).** c) **If \( h(x) = g(f(x)) \), find \( h'(3) \).** These problems require applying derivative rules such as the product rule, quotient rule, and chain rule to find the derivatives and evaluate them at \( x = 3 \).
Transcribed Image Text:The image presents a set of calculus problems involving derivatives with given functions and their values at specific points. **Given Information:** - \( f(3) = 5 \) - \( g(3) = -4 \) - \( f'(3) = -2 \) - \( g'(3) = 7 \) - \( f'(5) = 3 \) - \( g'(5) = 10 \) **Problems:** a) **If \( h(x) = f(x)g(x) \), find \( h'(3) \).** b) **If \( h(x) = \frac{f(x)}{g(x)+1} \), find \( h'(3) \).** c) **If \( h(x) = g(f(x)) \), find \( h'(3) \).** These problems require applying derivative rules such as the product rule, quotient rule, and chain rule to find the derivatives and evaluate them at \( x = 3 \).
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