   Chapter 9.9, Problem 2CP ### 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

# Suppose the total cost function for a commodity is C ( x )   =   0.01 x 3 — 0.9 x 2 +   33 x +   3000. What is the marginal cost if x = 50 units are produced?

To determine

To calculate: The marginal cost if x=50 units are produced for the cost function C(x)=0.01x30.9x2+33x+3000.

Explanation

Given Information:

The total cost function is C(x)=0.01x30.9x2+33x+3000.

Formula used:

Power of x rule for function f(x)=xn is f(x)=nxn1, where n is a real number.

Coefficient rule for a constant c is such that, if f(x)=cu(x), where u(x) is a differentiable function of x, then f(x)=cu(x).

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

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

MC¯=C(x)

Calculation:

Consider the total cost function,

C(x)=0.01x30.9x2+33x+3000

Differentiate both sides with respect to x,

C(x)=ddx(0.01x30.9x2+33x+3000)=ddx(0.01x3)ddx(0

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