   Chapter 11.4, Problem 79E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Fuel Economy (You saw this exercise in Section 11.3. This time, use the chain rule to calculate the derivative.) Your muscle car’s gas mileage (in miles per gallon) is given as a function M ( x ) ofspeed x in miles per hour, where M ( x ) = 3 , 000 x + 3 , 600 x − 1 . Calculate M ' ( x ) andthen M ' ( 10 ) , M ' ( 60 ) , and  M ' ( 70 ) . What do the answer tell you about your car?

To determine

To calculate: The values of M(x), M(10), M(60), M(70) and determine what the answers tell if it is given that the muscle car’s gas mileage(in miles per gallon) is given by the function M(x)=3000x+3600x1 where M(x) is the function of speed x in miles per hour.

Explanation

Given Information:

The muscle car’s gas mileage (in miles per gallon) is given by the function M(x)=3000x+3600x1 where M(x) is the function of speed x in miles per hour.

Formula used:

Derivative of function f(x)=(u)n using chain rule is f'(x)=ddx(u)n=nun1dudx, where u is the function of x.

Calculation:

Consider the function, M(x)=3000x+3600x1

Apply the chain rule,

M(x)=ddx3000(x+3600x1)1=3000(1)(x+3600x1)2ddx(x+3600x1)=3000(x+3600x1)2(13600x2)=3000(13600x2)(x+3600x1)2

Substitute x=10 in the function M(x)=3000(13600x2)(x+3600x1)2 as,

M(10)=3000(13600(10)2)((10)+3600(10)1)2=105000136900=0.767

The value of M(10) is 0.767

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