   Chapter 9.9, Problem 20E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# If the cost function for a commodity is C ( x )   =   1 90 x 3 +   4 x 2 + 4 x +   10 dollars find the marginal cost at x =   3 units and tell what this predicts about the cost of producing 1 additional unit and 2 additional units.

To determine

To calculate: The marginal cost, at x=3 units, for the cost function, C(x)=190x3+4x2+4x+10. Also, find the cost for producing additional 1 unit and 2 units.

Explanation

Given Information:

The cost function is C(x)=190x3+4x2+4x+10.

Formula used:

According to the power rule, if f(x)=xn, then,

f(x)=nxn1

According to the property of differentiation, if a function is of the form, g(x)=cf(x), then,

g(x)=cf(x)

According to the property of differentiation, if a function is of the form f(x)=u(x)+v(x), then,

f(x)=u(x)+v(x)

The derivative of a constant value, k, is

ddx(k)=0

Calculation:

Consider the marginal cost function to be MC¯. Consider the provided cost function,

C(x)=190x3+4x2+4x+10

The marginal cost of a cost function is found by differentiating the cost function.

MC¯=C(x)

Thus, differentiate both sides of the cost function with respect to x,

C(x)=ddx(190x3+4x2+4x+10)MC¯=ddx(190x3)+ddx(4

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