Chapter 9, Problem 96RE

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Chapter
Section

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

# Demand The demand q for a product at price p is given by q = 10 , 000 − 50 0.02 p 2 + 500 Find the rate of change of demand with respect to price.

To determine

To calculate: The rate of change of demand represented by the function, q=10000500.02p2+500, for a product with price p.

Explanation

Given Information:

The provided function for demand is q=10000âˆ’500.02p2+500, where p is the price.

Formula used:

According to the power rule, if f(x)=xn, then,

fâ€²(x)=nxnâˆ’1

According to the property of differentiation, if a function is of the form, g(x)=cf(x), then,

gâ€²(x)=cfâ€²(x)

According to the property of differentiation, if a function is of the form f(x)=u(x)+v(x), then,

fâ€²(x)=uâ€²(x)+vâ€²(x)

According to the chain rule of derivatives, for a function of form, y=f(u(x)), the derivative is

dydx=fâ€²(u(x))â‹…uâ€²(x)

Calculation:

Consider the provided demand function,

q=10000âˆ’500.02p2+500

Rewrite the function,

q=10000âˆ’50(0.02p2+500)12

To find the rate of change of demand, differentiate both sides with respect to p,

dqdp=ddp(10000âˆ’50(0.02p2+500)12)=ddp(1000)âˆ’ddp(50(0.02p2+500)12)=ddp(1000)âˆ’50ddp((0

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started