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Find (ƒ + g)'(3) and (ƒ — g)'(0). Find (fg)' (2) and (f/g)'(1). Find (fog)'(0) and (gof)' (2).

Find (ƒ + g)'(3) and (ƒ — g)'(0). Find (fg)' (2) and (f/g)'(1). Find (fog)'(0) and (gof)' (2).

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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4. Assume that \( f \) and \( g \) are differentiable functions for which the following is known. - \( f(0) = 1, \, f(1) = 2, \, f(2) = 3, \) and \( f(3) = 0. \) - \( f'(0) = 0, \, f'(1) = 2, \, f'(2) = 3, \) and \( f'(3) = 1. \) - \( g(0) = 2, \, g(1) = 3, \, g(2) = 0, \) and \( g(3) = 1. \) - \( g'(0) = 1, \, g'(1) = 0, \, g'(2) = 3, \) and \( g'(3) = 2. \) A. Find \( (f + g)'(3) \) and \( (f - g)'(0) \). B. Find \( (fg)'(2) \) and \( \left(\frac{f}{g}\right)'(1) \). C. Find \( (f \circ g)'(0) \) and \( (g \circ f)'(2) \).
Transcribed Image Text:4. Assume that \( f \) and \( g \) are differentiable functions for which the following is known. - \( f(0) = 1, \, f(1) = 2, \, f(2) = 3, \) and \( f(3) = 0. \) - \( f'(0) = 0, \, f'(1) = 2, \, f'(2) = 3, \) and \( f'(3) = 1. \) - \( g(0) = 2, \, g(1) = 3, \, g(2) = 0, \) and \( g(3) = 1. \) - \( g'(0) = 1, \, g'(1) = 0, \, g'(2) = 3, \) and \( g'(3) = 2. \) A. Find \( (f + g)'(3) \) and \( (f - g)'(0) \). B. Find \( (fg)'(2) \) and \( \left(\frac{f}{g}\right)'(1) \). C. Find \( (f \circ g)'(0) \) and \( (g \circ f)'(2) \).
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