Chapter 10.2, Problem 21E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

In Problems 21-24, a function and its first and second derivatives are given. Use these to find relative maxima, relative minima, and points of inflection; sketch the graph of each function.

To determine

**To calculate:** The relative minimum, relative maximum and points of inflection for the provided equation

Explanation

**Given Information:**

The provided equation is

**Formula used:**

To find relative maxima and minima of a function,

Step 1. Set the first derivative of the function to zero,

Step 2. Substitute the critical values into

Step 3. Evaluate

If

If

If

**Calculation:**

Consider the provided equation,

Now, consider the first derivative

Now, to obtain the critical values, set

Consider, if the denominator is 0, the function is not defined.

Thus, 0 is a critical point.

Consider either

First consider

Add

Thus, the critical values of the equation are at

Now, substitute

Substitute

Thus, the critical points are

Now, consider the second derivative

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