   Chapter 9.9, Problem 13E ### 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

# In Problems 9-16, cost is in dollars and x is the number of units. Find the marginal cost functions for the given cost functions. 13.   C   = x 3 − 6 x 2 + 24 x + 10

To determine

To calculate: The marginal cost function for the given total cost function C(x)=x36x2+24x+10.

Explanation

Given Information:

The given total cost function is C(x)=x36x2+24x+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 provided cost function,

C(x)=x36x2+24x+10

The marginal cost is found by differentiating the cost function and denoted by MC¯ as,

MC¯=C

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