   Chapter 5.1, Problem 62E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

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

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Profit In Exercises 61–64, find the profit function for the given marginal profit and initial condition. Marginal   Profit Initial   Condition d P d x = − 40 x + 250 P ( 5 ) = $650 To determine To calculate: The profit function for the marginal profit dPdx=40x+250 with initial condition P(5)=$650.

Explanation

Given Information:

The marginal profit is dPdx=40x+250 and initial condition is P(5)=\$650.

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.

Calculation:

Consider the marginal profit, dPdx=40x+250.

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

dpdxdx=(40x+250)dx=40xdx+250dx

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

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