Chapter 5.1, Problem 61E

### 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
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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 = − 18 x + 1650 P ( 15 ) = $22 , 725 To determine To calculate: The profit function for the marginal profit dPdx=18x+1650 with initial condition P(15)=$22725.

Explanation

Given Information:

The marginal profit is dPdx=18x+1650 and initial condition is P(15)=\$22725.

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=18x+1650.

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

dpdxdx=(18x+1650)dx=18xdx+1650dx

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

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