Chapter 10, Problem 2T

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

Find the relative maxima, relative minima, points of inflection, and asymptotes, if they exist, for each of the functions in Problems 1-3. Graph each function.

To determine

**To calculate:** The relative minimum, relative maximum, points of inflection and asymptotes for the function

Explanation

**Given Information:**

The provided function is,

**Formula used:**

A vertical asymptote of a function

A vertical asymptote of a rational function

A horizontal asymptote of a function

A horizontal asymptote of a rational function

1. A line

2. The line

3. Does not exist if the degree of the numerator is greater than the degree of the denominator.

To find relative maxima and minima of a function,

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

2. Substitute the critical values into

3. Calculate the sign of the function to the left and right of the critical values.

(a) If

(b) If

**Calculation:**

Consider the provided function,

Now, calculate the first derivative.

Now, to obtain the critical values, set

Thus, either

First consider

Add *x* to both sides and simplify:

And,

Thus, the critical values of the function are at

Now, substitute

Substitute

Thus, the critical points are

Now, calculate the sign of the

First consider

Calculate

Thus,

Calculate

Thus,

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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