Explanation Given information: The function: F ( x ) = x + 3 and a = 1 Calculation: We are given the function F ( x ) = x + 3 and a = 1 We know that for a function f ( x ) the linear approximation of the function at x = a is given by: f ( x ) ≈ f ( a ) + f ' ( a ) ( x − a ) The quadratic approximation of the function is given by: y = f ( a ) + f ' ( a ) ( x − a ) + 1 2 f ' ' ( a ) ( x − a ) 2 For the given f ( x ) : f ' ( x ) = 1 2 x + 3 → f ' ( 1 ) = 1 4

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Chapter 3.8, Problem 39E

To determine

To find: the quadratic approximation to F(x)=x+3 near a = 1 and graph f , the quadratic approximation and the linear approximation from 1 on a common screen.

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Chapter 3.8, Problem 38E

Chapter 3.8, Problem 40E

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the quadratic approximation to F ( x ) = x + 3 near a = 1 and graph f , the quadratic approximation and the linear approximation from 1 on a common screen.

Solution Summary: The author compares the quadratic and linear approximations of the functions on a common screen.

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To find: the quadratic approximation to F(x)=x+3 near a = 1 and graph f , the quadratic approximation and the linear approximation from 1 on a common screen.

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