Chapter 10.1, Problem 53E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

** Production costs** Suppose that the average cost, in dollars, of producing a shipment of a certain product is

*x* is the number of machines used in the production process.

(a) Find the critical values of this function.

(b) Over what interval does the average cost decrease?

(c) Over what interval does the average cost increase?

**(a)**

To determine

**To calculate:** The critical values of the function *x* is the number of machines used in the product process.

Explanation

**Given Information:**

The provided equation is

**Formula Used:**

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.

As per the First Derivative Test,

The first derivative of the function is evaluated. The first derivative is made equal to zero in order to get the critical points.

The values of the critical values are kept inside the original function which gives the critical points. The intervals of the values of x are then evaluated for the relative maximum and minimum.

**Calculation:**

Consider the provided equation

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.

Hence, there will no change in the values of critical values as in the derivative graph

**(b)**

To determine

**To calculate:** The values of *x* for which the function *x* is the number of machines used in the product process.

**(c)**

To determine

**To calculate:** The values of *x* for which the function *x* is the number of machines used in the product process.

Sect-10.1 P-1CPSect-10.1 P-2CPSect-10.1 P-3CPSect-10.1 P-4CPSect-10.1 P-1ESect-10.1 P-2ESect-10.1 P-3ESect-10.1 P-4ESect-10.1 P-5ESect-10.1 P-6E

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