Chapter 10.1, Problem 27E

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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, relative minima, or horizontal points of inflection by observing the graph

Explanation

**Given Information:**

The provided function is

**Formula Used:**

To obtain the relative maxima and minima of a function,

1. Find the first derivative of the function.

2. Set the derivative equal to

3. Evaluate

(a) If

(b) If

**Explanation:**

Consider the provided function

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.

Take out the first derivative of the equation by the power rule,

Put the value of

Evaluate the values of *x* from the equation:

Hence, the value(s) of *x* are

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

Put

Hence,

Put

Hence,

Test the derivative at the left and right sides of all the critical points.

Left of -6 is

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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