Chapter 10, Problem 39RE

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

** Output** The following figure shows a typical graph of output

(a) Is the point of diminishing returns closest to the point at which

(b) The average output per dollar of capital investment is defined as the total output divided by the amount of capital investment; that is,

Average output =

Calculate the slope of a line from (0, 0) to an arbitrary point

(c) Is the maximum average output attained when the capital investment is closest to

**(a)**

To determine

The capital investment at which the point of diminishing returns to closest among

Explanation

**Given Information:**

The provided graph of the capital investment and the output is shown below:

**Explanation:**

The critical values are the only values at which the graph can have turning points, the derivative cannot change sign anywhere except at the critical value.

This, in an interval between two critical values, the sign of the derivative at any value in the interval will be the sign of the derivative at all values in the interval.

If the first derivative of *f* is 0 at *x* passes through

**(b)**

To determine

**To calculate:** The slope of a line from *y* (in thousands of dollars) as a function of capital investment I where the average output is,

.

**(c)**

To determine

The maximum average point attained at *y* (in thousands of dollars) as a function of capital investment I.

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