Chapter 10.1, Problem 23E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

For each function and graph in Problems 21-24

(a) use the graph to identify *x*-values for which
*yâ€™* does not exist.

(b) use the derivative to check your conclusions.

**(a)**

To determine

The *x*-values where

Explanation

**Given Information:**

The provided function is

**Explanation:**

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.

This, in an interval between two critical values, the sign of the derivative at any value in the interval will be the sign of the derivative at all values in the interval.

As per the First Derivative Test,

The first derivative of the function is evaluated. The first derivative is made equal to zero in order to get the critical points.

The values of the critical values are kept inside the original function which gives the critical points. The intervals of the values of x are then evaluated for the relative maximum and minimum.

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)**

To determine

**To calculate:** The conclusions from the derivative where the function

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