   Chapter 11.2, Problem 43E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

If the marginal cost is decreasing, is the average cost necessarily decreasing? Explain.

To determine

Whether the average cost is necessarily decreasing if the marginal cost is decreasing and explain the answer.

Explanation

Given Information:

The provided marginal cost is decreasing.

Assume the function,

C(x)=2x2+500

As marginal cost is C(x)

So, calculate the marginal cost if the function,

C(x)=ddx(2x2+500)

Sum rule of the derivative is ddx[f(x)+g(x)]=ddx[f(x)]+ddx[g(x)] where f(x) and g(x) are any two differentiable functions.

Constant multiple rules of the derivative are f(cx)=cf(x), where c is any constant.

Apply sum rule and constant multiple rules of the derivative in C(x)=ddx(2x2+500),

C(x)=2ddx(x2)+500ddx(1)

A derivative of a function y=xn using power rule is dydx=nxn1

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