Chapter 10.5, Problem 18E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

For each function in Problems 11-18, find any horizontal and vertical asymptotes, and use information from the first derivative to sketch the graph.

To determine

**To calculate:** The horizontal and vertical for the provided function

Explanation

**Given Information:**

The provided function is

**Formula used:**

A vertical asymptote of a rational function

A horizontal asymptote of a rational function

Step 1. A line

Step 2. The line

Step 3. Does not exist 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.

If

If

**Calculation:**

Consider the provided function,

Recall that a vertical asymptote of a rational function

Set the denominator

Which is not possible.

Thus, there is no vertical asymptote.

Degree of the numerator is 2 and denominator is 4 of the function

Since, the degree of the numerator is less than the denominator.

Thus, the horizontal asymptote is

Now, calculate the first derivative of the function

Now, to obtain the critical values, set

Thus, either

First consider

Solve for *x*.

Now consider

Solve for *x*.

Now consider

Solve for *x*.

Thus, the critical points are

Now, calculate the sign of the

First consider

Calculate

Thus,

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