   Chapter 9, Problem 96RE Mathematical Applications for the ...

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

Solutions

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=10000500.02p2+500, where p is the price.

Formula used:

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

f(x)=nxn1

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

g(x)=cf(x)

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

f(x)=u(x)+v(x)

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

dydx=f(u(x))u(x)

Calculation:

Consider the provided demand function,

q=10000500.02p2+500

Rewrite the function,

q=1000050(0.02p2+500)12

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

dqdp=ddp(1000050(0.02p2+500)12)=ddp(1000)ddp(50(0.02p2+500)12)=ddp(1000)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

Let f be the function defined by f(x)={x2+1ifx0xifx0 Find f(2), f(0), and f(1).

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

What graph has f′(2) > 0 and f″(2) < 0?

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Find the unit tangent vector for at t = –1.

Study Guide for Stewart's Multivariable Calculus, 8th 