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Problem 1. The figure below shows f(x) and its local linearization at x = a. Note that I have already provided you with the linear approximation. Also note that the y-axis scale goes by ones. 1. What is the value of a? 2. What is the value of f(a)? 3. Is the approximation an under- or overestimate? 4. Use the linearization to approximate f(1.2). Y 1 f(x) 2 y=2x-1

Problem 1. The figure below shows f(x) and its local linearization at x = a. Note that I have already provided you with the linear approximation. Also note that the y-axis scale goes by ones. 1. What is the value of a? 2. What is the value of f(a)? 3. Is the approximation an under- or overestimate? 4. Use the linearization to approximate f(1.2). Y 1 f(x) 2 y=2x-1

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 1. The figure below shows \( f(x) \) and its local linearization at \( x = a \). Note that I have already provided you with the linear approximation. Also note that the \( y \)-axis scale goes by ones. 1. What is the value of \( a \)? 2. What is the value of \( f(a) \)? 3. Is the approximation an under- or overestimate? 4. Use the linearization to approximate \( f(1.2) \). **Graph Explanation:** The graph includes a function \( f(x) \) and the line \( y = 2x - 1 \) representing its local linear approximation. - The function \( f(x) \) is shown as a curve, and the line \( y = 2x - 1 \) is a tangent approximation at a certain point. - The x-axis is labeled from 0 to 2, with a specific point noted at \( x = 1 \). - The y-axis has equal increments, with each unit marked by grid lines. The curve and the tangent line intersect at a specific point, illustrating the concept of linearization at \( x = a \).
Transcribed Image Text:Problem 1. The figure below shows \( f(x) \) and its local linearization at \( x = a \). Note that I have already provided you with the linear approximation. Also note that the \( y \)-axis scale goes by ones. 1. What is the value of \( a \)? 2. What is the value of \( f(a) \)? 3. Is the approximation an under- or overestimate? 4. Use the linearization to approximate \( f(1.2) \). **Graph Explanation:** The graph includes a function \( f(x) \) and the line \( y = 2x - 1 \) representing its local linear approximation. - The function \( f(x) \) is shown as a curve, and the line \( y = 2x - 1 \) is a tangent approximation at a certain point. - The x-axis is labeled from 0 to 2, with a specific point noted at \( x = 1 \). - The y-axis has equal increments, with each unit marked by grid lines. The curve and the tangent line intersect at a specific point, illustrating the concept of linearization at \( x = a \).
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