   Chapter 4.8, Problem 41E Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Solutions

Chapter
Section Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

Stopping Distance The total stopping distance T of a vehicle is T = 2.5 x + 0.5 x 2 where T is in feet and x is the speed in miles per hour. Approximate the change and percent change in total stopping distance as speed changes from x = 25   to   x = 26 miles per hour.

To determine

To calculate: The change and percentage change in the stopping distance.

Explanation

Given:

The stopping distance is given by the formula:

T=2.5x+0.5x2

The value of x changes from 25 to 26.

Formula used:

The approximate change in the function f is given by the formula:

df=f'(x)dx

Calculation:

Consider the formula for stopping distance:

T=2.5x+0.5x2

Differentiate this with respect to x to obtain:

T'(x)=2.5+x

Here,

x=25x=2625=1

Now,

dT=T'(x)dx=(2

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