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: 9781319309671

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 4.1, Problem 54E

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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 4.1, Problem 53E

Chapter 4.1, Problem 55E

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Let f(a, y) = 3x² + 4y2 – axy. (a) Find the values of a such that the graph of f increases when moving from the point (1, 2) in the positive x-direction. (b) Find the values of a such that the graph of f increases when moving from the point (1, 2) in the positive y-direction.

Consider the linearizable functions as follows. Find new transformed variables (x, y, B or B as you need) to linearize the functions below. 21 y= Biz1+ Bo.

Chapter 4 Solutions

CALCULUS: EARLY TRANS 4TH ED W/ ACCESS

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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