Chapter 9.9, Problem 1CP

### 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

# Suppose the total cost function for a commodity is C ( x )   =   0.01 x 3 — 0.9 x 2 +   33 x +   3000 .Find the marginal cost function.

To determine

To calculate: The marginal cost function if the total cost function is C(x)=0.01x30.9x2+33x+3000.

Explanation

Given Information:

The total cost function is C(x)=0.01x3âˆ’0.9x2+33x+3000.

Formula used:

Power of x rule for function f(x)=xn is fâ€²(x)=nxnâˆ’1, where n is a real number.

Coefficient rule for a constant c is such that, if f(x)=câ‹…u(x), where u(x) is a differentiable function of x, then fâ€²(x)=câ‹…uâ€²(x).

Constant function rule for a constant c is such that, if f(x)=c then fâ€²(x)=0.

The marginal cost of a cost function is provided by derivative of total cost function C(x),

MCÂ¯=Câ€²(x)

Calculation:

Consider the total cost function,

C(x)=0.01x3âˆ’0.9x2+33x+3000

Differentiate both sides with respect to x,

Câ€²(x)=ddx(0.01x3âˆ’0.9x2+33x+3000)=ddx(0

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