Explanation Given: The function is f ( x ) = 3 x − 4 , where a = 0 and a = 2 . Formula used: The formula of linearization L ( x ) , centered at x = 1 is: L ( x ) = f ′ ( a ) ( x − a ) + f ( a ) Calculation: The function is f ( x ) = 3 x − 4 , where a = 0 and a = 2 . Differentiate the function with respect to x . f ′ ( x ) = 3 x − 4 = 3 Find the linearization at a = 0 . L ( x ) = f ′ ( a ) ( x − a ) + f ( a ) Substitute 0 for a in the above formula

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 4.1, Problem 54E

To determine

Find the linearization of f(x)=3x−4 at a=0 and a=2. Also, prove more generally that a linear function coincides with its linearization at x=a for all a.

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Chapter 4.1, Problem 53E

Chapter 4.1, Problem 55E

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Chapter 4 Solutions

Calculus: Early Transcendentals

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

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Find the linearization of f ( x ) = 3 x − 4 at a = 0 and a = 2 . Also, prove more generally that a linear function coincides with its linearization at x = a for all a.

Solution Summary: The author explains how to find the linearization of f(x)=3x-4 at a=0.

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Find the linearization of f(x)=3x−4 at a=0 and a=2. Also, prove more generally that a linear function coincides with its linearization at x=a for all a.

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Chapter 4 Solutions