Chapter 10.2, Problem 19E

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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 function

Explanation

**Given Information:**

The provided function 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 function,

Now, consider the first derivative

Now, to obtain the critical values, set

Thus, either

First consider

Thus,

Subtract

Now consider

Add

And,

Thus, the critical values of the function are at

Now, substitute

Substitute

And, substitute

Thus, the critical points are

Now, consider the second derivative

To obtain point of inflection, set

Thus, either

First consider

Add

And,

Now, substitute

Now, substitute

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