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Let g(x) = sin [f(x + 1) - 3] + 2x, where f is a continuous function with f(2) = 3. The graph of the derivative of f on the interval [-2, 7] is given below. 5 4 3 2 1 21, 2 y f'(x) 1 2 3 4 5 Use a linearization of g to approximate g(1.01). Round to 2 decimal places.

Let g(x) = sin [f(x + 1) - 3] + 2x, where f is a continuous function with f(2) = 3. The graph of the derivative of f on the interval [-2, 7] is given below. 5 4 3 2 1 21, 2 y f'(x) 1 2 3 4 5 Use a linearization of g to approximate g(1.01). Round to 2 decimal places.

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 3** Let \( g(x) = \sin [f(x + 1) - 3] + 2x \), where \( f \) is a continuous function with \( f(2) = 3 \). The graph of the derivative of \( f \) on the interval \([-2, 7]\) is given below. ![Graph of the derivative of function f] The graph below shows the derivative function \( f'(x) \) plotted on a coordinate plane with the \( x \)-axis ranging from \(-2\) to \(6\) and the \( y \)-axis ranging from \(-2\) to \(5\). 1. **x-axis (horizontal axis)**: Labeled from \(-2\) to \(6\). 2. **y-axis (vertical axis)**: Labeled from \(-2\) to \(5\). The graph of \( f'(x) \) is a linear function passing through the following points: - From \((-2, -1)\) to \((3, 5)\), the graph is a line with a positive slope. - From \((3, 5)\) to \((6, -1)\), the graph is a line with a negative slope. Below the graph, the instruction states: "Use a linearization of \( g \) to approximate \( g(1.01) \). Round to 2 decimal places."
Transcribed Image Text:**Question 3** Let \( g(x) = \sin [f(x + 1) - 3] + 2x \), where \( f \) is a continuous function with \( f(2) = 3 \). The graph of the derivative of \( f \) on the interval \([-2, 7]\) is given below. ![Graph of the derivative of function f] The graph below shows the derivative function \( f'(x) \) plotted on a coordinate plane with the \( x \)-axis ranging from \(-2\) to \(6\) and the \( y \)-axis ranging from \(-2\) to \(5\). 1. **x-axis (horizontal axis)**: Labeled from \(-2\) to \(6\). 2. **y-axis (vertical axis)**: Labeled from \(-2\) to \(5\). The graph of \( f'(x) \) is a linear function passing through the following points: - From \((-2, -1)\) to \((3, 5)\), the graph is a line with a positive slope. - From \((3, 5)\) to \((6, -1)\), the graph is a line with a negative slope. Below the graph, the instruction states: "Use a linearization of \( g \) to approximate \( g(1.01) \). Round to 2 decimal places."
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