Explanation Given: 16.2 Linearization L ( x ) of f ( x ) = x at a = 16 Concepts: Suppose that y = f ( x ) is a differentiable curve at x = a . Then the tangent line at x = a has equation y = f ( a ) + f ' ( a ) ( x − a ) We call the above equation the linear approximation or linearization of y = f ( x ) at the point ( a , f ( a ) ) and write f ( x ) ≈ L ( x ) = f ( a ) + f ' ( a ) ( x − a ) We sometimes write L a ( x ) to stress that the approximation is near a . Calculation: Description Step 1:Consider the function Let f ( x ) = x 1 / 2 , a = 16 a n d Δ x = 0

CALCULUS EARLY TRANSCENDENTALS W/ACHIEVE

4th Edition

ISBN: 9781319057664

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 4.1, Problem 55E

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Whether the given estimate from the Linear Approximation is too large or too small

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Chapter 4.1, Problem 54E

Chapter 4.1, Problem 56E

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Chapter 4 Solutions

CALCULUS EARLY TRANSCENDENTALS W/ACHIEVE

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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Whether the given estimate from the Linear Approximation is too large or too small

Solution Summary: The author describes the linear approximation of y =f(x) at the point (a,f)

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