Chapter 10.1, Problem 30E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

For each function in Problems 25-30, find the relative maxima, relative minima, and horizontal points of inflection; then sketch the graph. Check your graph with a graphing utility.

To determine

**To calculate:** The relative maxima, minima and horizontal points of inflection for the provided function

Explanation

**Given Information:**

The provided function is,

**Formula used:**

To obtain the relative maxima and minima of a function,

Step 1. Find the first derivative of the function.

Step 2. Set the derivative equal to

Step 3. Evaluate

If

If

**Calculation:**

Consider the provided function,

Now, obtain its derivative as,

Now, set

Thus,

And,

Now, substitute

And, substitute

Thus, the critical points are

Now, obtain the left and right behavior of these critical points.

Thus, substitute

Substitute

Substitute

Thus,

Therefore, relative maximum occurs at

Also, obtain the second derivative as,

Now, set

Thus,

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