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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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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 = 24 x + 805 P ( 12 ) = $ 8000

To determine

To calculate: The profit function for the marginal profit dPdx=24x+805 with initial condition P(12)=$8000.

Explanation

Given Information:

The marginal profit is dPdx=24x+805 and initial condition is P(12)=$8000.

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=24x+805.

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

dpdxdx=(24x+805)dx=24xdx+805dx

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

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