Explanation Given: The function is F ( s ) = 1.1 s + 0.054 s 2 ft . Formula used: Linear approximation of Δ f : If f is differentiable at x = a and Δ x is small then Δ f ≈ f ′ ( a ) Δ x Where Δ f = f ( a + Δ x ) − f ( a ) . Calculation: Consider the function F ( s ) = 1.1 s + 0.054 s 2 ft . Differentiate the function with respect to x . F ′ ( s ) = 1.1 + 0.054 ( 2 s 2 − 1 ) = 1.1 + 0.108 s Find the value of Δ F when a = 35 . Now, apply the linear approximation with a = 35 and Δ s = 1 . Use the formula: Δ F ≈ F ′ ( a ) Δ s Δ F ≈ F ′ ( a ) Δ s = F ′ ( 35 ) ( 1 ) = ( 1

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Question

Chapter 4.1, Problem 36E

To determine

Find the change in stopping distance per additional mph when s=35 and when s=55 by using linear approximation.

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Chapter 4.1, Problem 35E

Chapter 4.1, Problem 37E

Chapter 4 Solutions

CALCULUS (CLOTH)

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Find the change in stopping distance per additional mph when s = 35 and when s = 55 by using linear approximation.

Solution Summary: The author explains the linear approximation of Delta f and the formula for it.

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Find the change in stopping distance per additional mph when s=35 and when s=55 by using linear approximation.

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Chapter 4 Solutions