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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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Checkpoint 8 Worked-out solution available at LarsonAppliedCalculus.com

The marginal cost of producing x units of a product is modeled by

d C d x = 28 0.02 x .

It costs $40 to produce one unit. Find the cost of producing 200 units.

To determine

To calculate: The cost of producing 200 units, when the marginal cost of producing x units is modeled as, dCdx=280.02x. If the cost to produce one unit is $40.

Explanation

Given Information:

The marginal cost of producing x units of a product is dCdx=280.02x. The cost of producing one unit is $40.

Formula used:

The difference rule of integration [f(x)g(x)]dx=f(x)dxg(x)dx.

The simple power rule of integration, xndx=xn+1n+1+C.

Calculation:

Consider the marginal cost, dCdx=280.02x.

Integrate the provided rate of marginal cost.

(dCdx)dx=(280.02x)dx

Rewrite the above indefinite integral, use the difference integral rule, [f(x)g(x)]dx=f(x)dxg(x)dx.

(dCdx)dx=(280.02x)dx=28dx(0.02x)dx

Integrate the provided indefinite integral, use the simple power rule of integration xndx=xn+1n+1+C

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