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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
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) > 0 if p′(x) is greater than the average productivity.

(a)

To determine

To find: The value of A'(x) and the reason that why the company wants to hire more workers if A'(x)>0.

Explanation

Given:

The average productivity of the workforce at the plant is shown below with an equation.

A(x)=p(x)x (1)

Calculation:

Calculate the value of A'(x).

Differentiate equation (1) with respect to x.

Apply the quotient rule below.

(uv)'=u'vv'uv2

Substitute p(x) for u and x for v in the above equation.

(p(x)x)=p'(x)x(1)<

(b)

To determine

To show: The condition A'(x)>0 is true, if the expression p'(x) is greater than the average productivity.

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