(a) Explanation Given information: The given function is y = f ( x ) = 2 x + 1 . Formula used: The formula to calculate the differential of a function h ( x ) = [ g ( x ) ] n by General Power Rule is, h ′ ( x ) = n [ g ( x ) ] n − 1 g ′ ( x ) The formula to calculate the differential of a function h ( x ) = g [ f ( x ) ] by Chain Rule is, d d x g [ f ( x ) ] = g ' [ f ( x ) ] ⋅ f ' ( x ) Calculation: Differentiate the function f ( x ) = 2 x + 1 with respect to x on both sides. f ′ ( x ) = d d x ( 2 x + 1 ) = d d x [ ( 2 x + 1 ) 1 2 ] &# (b) To determine The approximate change in the function y if x changes from 4 to 4.1. (c) To determine To find: The actual change in the function y for change in x from 4 to 4.1.

Applied Calculus for the Managerial, Life, and Social Sciences

10th Edition

ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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Question

Chapter 3.7, Problem 18E

(a)

To determine

To find: The differential of the given function.

(b)

To determine

The approximate change in the function y if x changes from 4 to 4.1.

(c)

To determine

To find: The actual change in the function y for change in x from 4 to 4.1.

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Chapter 3.7, Problem 17E

Chapter 3.7, Problem 19E

Chapter 3 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences

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The differential of the given function.

Solution Summary: The author explains the formula to calculate the differential of a function sqrt2x+1.

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To find: The differential of the given function.

The approximate change in the function y if x changes from 4 to 4.1.

To find: The actual change in the function y for change in x from 4 to 4.1.

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Chapter 3 Solutions