   Chapter 10.1, Problem 50E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Pricing and sales Suppose that a chain of auto service stations, Quick-Oil, Inc., has found that its monthly sales volume y (in thousands of dollars) is related to the price p (in dollars) of an oil change by y = 90 p + 5 , p > 10 Is y increasing or decreasing for all values of p > 10?

To determine

Whether y increasing or decreasing for all values of p>10 if the chain of auto service stations Quick-Oil, Inc. has found that its monthly sales volume y which is in thousands of dollars, of an oil change by y=90p+5,p>10, where price p is in dollars.

Explanation

Given Information:

The provided function is y=90p+5,p>10.

Explanation:

Consider the provided equation y=90p+5,p>10,

The first derivative is made equal to zero in order to get the critical points.

The values of the critical values are kept inside the original function which gives the critical points. The intervals of the values of x are then evaluated for the relative maximum and minimum.

For differentiable function f on an interval (a,b),

If f(x)>0 the function f is increasing for all x in the interval (a,b).

If f(x)<0 the function f is decreasing for all x in the interval (a,b).

Take out the first derivative of the equation by the power rule,

ddp(y)=ddp(90p+5)=ddp(90(p+5)12)=ddp(90(p+5)(12))=90(12)(p+5)(12+1)

Solve further,

y=45(p+5)(32)=45(p+5)32

Put the value of

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