Explanation Formula used: The approximate change in function f ( x ) is, Δ [ f ( x ) ] = f ′ ( x ) Δ x (1) Calculation: The value of Δ x in function f ( x ) changes from a = 2 to b = 1.96 . Δ x = b − a = 1.96 − 2 = − 0.04 The function is, f ( x ) = 0.2 x 2 + 3.1 1.2 x + 1.3 . Differentiate above function with respect to x and get the value of f ′ ( x ) . d d x [ f ( x ) ] = d d x ( 0.2 x 2 + 3.1 1.2 x + 1.3 ) f ′ ( x ) = ( ( 1.2 x + 1.3 ) ( 0.2 × 2 x + 0 ) − ( 0.2 x 2 + 3.1 ) ( 1.2 + 0 ) ( 1.2 x + 1.3 ) 2 ) ( ∵ d ( u / v ) d x = v d u d x − u d v d x v 2 ) = ( ( 1.2 x + 1.3 ) ( 0.4 x ) − ( 0.2 x 2 + 3.1 ) ( 1.2 ) ( 1.2 x + 1.3 ) 2 ) = ( ( 0.48 x 2 + 0.52 x ) − ( 0.24 x 2 + 3.72 ) ( 1.2 x + 1.3 ) 2 ) Substitute ( ( 0

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 3.7, Problem 2TE

To determine

To find: The approximate value of the function f(x)=0.2x2+3.11.2x+1.3 when x changes from x=2 to x=1.96 .

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Chapter 3.7, Problem 1TE

Chapter 3.7, Problem 3TE

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Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

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The approximate value of the function f ( x ) = 0.2 x 2 + 3.1 1.2 x + 1.3 when x changes from x = 2 to x = 1.96 .

Solution Summary: The author calculates the approximate value of the function f(x)=0.2x

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To find: The approximate value of the function f(x)=0.2x2+3.11.2x+1.3 when x changes from x=2 to x=1.96 .

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Chapter 3 Solutions