Chapter 5.1, Problem 58E

### 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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# Finding a Cost Function In Exercises 55–58, find the cost function for the given marginal cost and fixed cost. See Example 8. Marginal   Cost Fixed   Cost   ( x = 0 ) d C d x = x 4 10 + 10 $2300 To determine To calculate: The cost function for the marginal cost dCdx=x410+10 that have a fixed cost of$2300.

Explanation

Given Information:

The marginal cost is dCdx=x410+10 and the fixed cost is \$2300.

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 cost, dCdx=x410+10.

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

dCdxdx=(x410+10)dxC(x)=x410dx+10dx=110x14dx+101dx

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

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