   Chapter 10.2, Problem 31E ### 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

# Productivity—diminishing returns The figure is a typical graph of worker productivity as a function of time on the job. (a) If P represents the productivity and t represents the time, write a mathematical symbol that represents the rate of change of productivity with respect to time.(b) Which of A, B, and C is the critical point for the rate of change found in part (a)? This point actually corresponds to the point at which the rate of production is maximized, or the point for maximum worker efficiency. In economics, this is called the point of diminishing returns.(c) Which of A, B, and C corresponds to the upper limit of worker productivity?

(a)

To determine

To calculate: The mathematical symbol for rate of change of productivity with respect to time if P represents the productivity and t represents time.

Explanation

Given Information:

The P represents the productivity and t represents time.

Calculation:

Consider P represents the productivity and t represents time.

Recall that rate of change of a function with respect to an independent variable is the derivative of that function with respect to that variable.

Thus, rate of change of productivity with respect to time is the derivative of the function P(t) with respect to t.

Differentiate P(t) with respect to t

(b)

To determine

To calculate: The critical point for the rate of change of productivity with respect to time if P represents the productivity and t represents time and the graph is, (c)

To determine

The point corresponds to the upper limit of worker productivity where the figure represents graph of worker productivity as a function of time on the job, ### Still sussing out bartleby?

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