Chapter 10.1, Problem 42E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

In Problems 37-42, use the derivative to locate critical points and determine a viewing window that shows all features of the graph. Use a graphing calculator to sketch a complete graph.

To determine

**To calculate:** The location of critical points from the derivation of the function

Explanation

**Given Information:**

The provided function is

**Formula Used:**

The simple power rule to derivative.

The steps to calculate the critical values of a function

Step 1: First find the derivative of the function.

Step 2: Equate the derivate of the function to 0 and calculate the possible critical points.

Step 3: Put the critical point in the provided function to get the critical values.

**Calculation:**

Consider the provided function

Use the simple power rule to differentiate,

Equate the above derivative to 0,

Evaluate the values of *x* from the equation:

From the property of zero multiplication,

Or,

Hence, the critical values of *x* are

Evaluate the values of the original functions with the critical values:

Substitute 0 for *x* in

Hence,

Substitute *x* in

Hence,

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