Chapter 10.5, Problem 11E

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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 if the degree of the numerator is greater than the degree of the denominator.

**Calculation:**

Consider the provided function,

Recall that a vertical asymptote of a rational function

Set the denominator

Substitute 3 for *x* in the numerator as below,

Thus, the vertical asymptote is the line

Degree of the numerator and denominator of the function

Thus, the horizontal asymptote is the line

Since, the leading coefficient in the numerator is 2 and in the denominator is 1.

Thus, the horizontal asymptote is,

Now, calculate the first derivative of the function

Now, to obtain the critical values, set

Which is not possible.

Thus, there are no critical points and hence no relative maximum or minimum.

Calculate

Thus, the point 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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