**3. Given the table, answer the following:** | | \( f(4) \) | \( f'(4) \) | \( g(4) \) | \( g'(4) \) | |-----|------------|-------------|------------|-------------| | | 2 | -3 | 5 | -1 | (a) Find the derivative of \( f \cdot g \) and \( \frac{f}{g} \) at \( x = 4 \). (b) Calculate \( F'(4) \), where \( F(x) = x \cdot f(x) \). (c) Calculate \( H'(4) \), where \( H(x) = \frac{x}{g(x)f(x)} \).
**3. Given the table, answer the following:** | | \( f(4) \) | \( f'(4) \) | \( g(4) \) | \( g'(4) \) | |-----|------------|-------------|------------|-------------| | | 2 | -3 | 5 | -1 | (a) Find the derivative of \( f \cdot g \) and \( \frac{f}{g} \) at \( x = 4 \). (b) Calculate \( F'(4) \), where \( F(x) = x \cdot f(x) \). (c) Calculate \( H'(4) \), where \( H(x) = \frac{x}{g(x)f(x)} \).
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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