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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Revenue and Demand In Exercises 59 and 60, find the revenue and demand functions for the given marginal revenue. (Use the fact that R = 0 when x = 0.)

d R d x = 225 3 x

To determine

To calculate: The revenue and demand functions for the marginal revenue dRdx=2253x when x=0 then R=0.

Explanation

Given Information:

The marginal revenue is dRdx=2253x and R=0 when x=0.

Formula used:

The sum rule of basic integration [f(x)+g(x)]dx=f(x)dx+g(x)dx.

The simple power rule of integration xndx=xn+1n+1+C.

The demand function of the company is given as, p=R(x)x where, p is the demand, R(x) is the revenue.

Calculation:

Consider the marginal revenue, dRdx=2253x.

Integrate the provided marginal cost, use the sum rule of basic integration [f(x)+g(x)]dx=f(x)dx+g(x)dx.

dRdxdx=(2253x)dx=225dx3xdx=2251dx3xdx

Use the simple power rule of integration xndx=xn+1n+1+C

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