   Chapter 2.7, Problem 31E

Chapter
Section
Textbook Problem

# If p(x) is the total value of the production when there are x workers in a plant, then the average productivity of the workforce at the plant is A ( x ) = p ( x ) x (a) Find A′(x). Why does the company want to hire more workers if a ′(x)>0?(b) Show that a ′(x) > 0if p'(x) is greater than the average productivity.

To determine

Part (a)

To find:

(i) A'(x)

(ii) Why does the company want to hire more workers if A'x> 0

Explanation

1) Formula:

Quotient rule: ddxuv=vu'-uv'v2

2) Given:

Ax=pxx

3) Calculation:

Differentiate Ax with respect to x

A'x=ddxpxx

By using quotient rule

A'x=x.p'x-px. x'x2

A'x=x

To determine

Part (b)

To show: if  p'(x) is greater than average productivity then A'x>0

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