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

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Chapter 5.2, Problem 52E
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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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Cost The marginal cost of a product is modeled by

d C d x  =  12 12 x   +   1 3 where x is the number of units. When x   = 13 ,   C = 100 .

(a) Find the cost function.

(b) Find the cost of producing 30 units.

Supply In Exercises 53 and 54, find the supply function x   =   f ( p ) that satisfies the initial condition.

(a)

To determine

To calculate: The cost function C where the marginal cost is modeled by the equation

dCdx=1212x+13 and when x=13, C=100.

Explanation

Given Information:

The marginal cost is modeled by the equation dCdx=1212x+13 and when x=13, C=100.

Formula Used:

According to the general power rule for integration,

If u is a differentiable function of x, then

∫undu=un+1n+1+C,

where n≠−1

Calculation:

Consider the equation dCdx=1212x+13.

Integrate dCdx to obtain C.

C=∫1212x+13dx=∫(12x+1)−13(12)dx

Apply the general power rule for integrtion in the above equation,

C=(12x+1)−13+1−13+1+k=(12x+1)2323+k=32

(b)

To determine

To calculate: The cost of producing 30 units from the cost function of part (a).

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