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7. Given the graph: (a) Given P(x) = f(x)g(x), find P′(2) f(x) (b) Given Q(x): find Q'(2) g(x)' = (c) Given C(x) = f(g(x)), find C'(2) YA 1 0 1 9 f X

7. Given the graph: (a) Given P(x) = f(x)g(x), find P′(2) f(x) (b) Given Q(x): find Q'(2) g(x)' = (c) Given C(x) = f(g(x)), find C'(2) YA 1 0 1 9 f X

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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## Problem 7 Given the graph: ### (a) Given \( P(x) = f(x)g(x) \), find \( P'(2) \). ### (b) Given \( Q(x) = \frac{f(x)}{g(x)} \), find \( Q'(2) \). ### (c) Given \( C(x) = f(g(x)) \), find \( C'(2) \). ### Graph Explanation The graph displays two piecewise linear functions \( f \) and \( g \) plotted on a coordinate grid. The x-axis ranges from 0 to 3, and the y-axis ranges from 0 to 3, with each unit marked by grid lines. - **Function \( g \)**: - Starts from point (0, 1). - Increases linearly to (1, 1). - Stays constant from x = 1 to x = 2. - Increases linearly from (2, 1) to (3, 2). - **Function \( f \)**: - Starts from point (0, 0). - Decreases linearly to (1, -1). - Increases linearly from (1, -1) to (2, 1). - Increases linearly again from (2, 1) to (3, 3).
Transcribed Image Text:## Problem 7 Given the graph: ### (a) Given \( P(x) = f(x)g(x) \), find \( P'(2) \). ### (b) Given \( Q(x) = \frac{f(x)}{g(x)} \), find \( Q'(2) \). ### (c) Given \( C(x) = f(g(x)) \), find \( C'(2) \). ### Graph Explanation The graph displays two piecewise linear functions \( f \) and \( g \) plotted on a coordinate grid. The x-axis ranges from 0 to 3, and the y-axis ranges from 0 to 3, with each unit marked by grid lines. - **Function \( g \)**: - Starts from point (0, 1). - Increases linearly to (1, 1). - Stays constant from x = 1 to x = 2. - Increases linearly from (2, 1) to (3, 2). - **Function \( f \)**: - Starts from point (0, 0). - Decreases linearly to (1, -1). - Increases linearly from (1, -1) to (2, 1). - Increases linearly again from (2, 1) to (3, 3).
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