Chapter 5.2, Problem 53E

### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

Chapter
Section

### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
1 views

# Supply In Exercises 53 and 54, find the supply function x   =   f ( p ) that satisfies the initial condition. d x d p  =  p p 2   −   25 x  = 600 when  p   =   $13 To determine To calculate: The supply function x=f(p) for which dxdp=pp225 that satisfies the initial condition x=600 when p=$13.

Explanation

Given Information:

The provided equation of derivative of the supply function is dxdp=pp225 and the initial

condition is x=600, when p=13.

Formula Used:

According to the general power rule for integration,

If u is a differentiable function of x, then

undu=un+1n+1+C

where n1

Calculation:

Consider the equation dxdp=pp225.

Integrate dxdp to obtain x.

x=pp225dp …… (1)

Let p225=u.

Differentiate with respect to p,

ddp(p225)=dudpddp(p2)ddp(25)=dudp2p=dudppdp=12du

Substitute the value of pdp=12du and p225=u in equation (1),

x=12udu

Now, apply the general power rule for integrtion in the above equation

x=12(u12+112+1)+C=12u32

### 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

#### In Exercises 13-20, sketch a set of coordinate axes and plot each point. 16. (3, 4)

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

#### In Problems 19-44, factor completely. 25.

Mathematical Applications for the Management, Life, and Social Sciences

#### True or False: If , then converge absolutely.

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

#### True or False: converges conditionally.

Study Guide for Stewart's Multivariable Calculus, 8th