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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 5.1, Problem 58E
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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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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=110∫x14dx+10∫1dx

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

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