Chapter 9.9, Problem 14E

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Chapter
Section

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
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. 14.   C = 0.1 x 3 − 1.5 x 2 + 15

To determine

To calculate: The marginal cost function for the total cost function, C(x)=0.1x31.5x2+9x+15.

Explanation

Given Information:

The total cost function is given as C(x)=0.1x3âˆ’1.5x2+9x+15.

Formula used:

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

fâ€²(x)=nxnâˆ’1

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

gâ€²(x)=cfâ€²(x)

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

fâ€²(x)=uâ€²(x)+vâ€²(x)

The derivative of a constant value, k, is

ddx(k)=0

Calculation:

Consider the provided cost function,

C(x)=0.1x3âˆ’1.5x2+9x+15

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

MCÂ¯=Câ€²(x)

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

Câ€²(x)=ddx(0

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