Chapter 4.6, Problem 59E

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Chapter
Section

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

# Analyzing the Graph of a Function Using TechnologyIn Exercises 55-62, use a computer algebra system to analyze and graph the function. Identify any relative extrema, points of inflection, and asymptotes. y = x 2 + ln x x + 3

To determine

To graph: The provided function y=x2+lnxx+3 with the help of a graphing utility and to obtain the extremas, inflection points and asymptotes for the function.

Explanation

Given:

y=x2+lnxx+3

Graph:

The graph of the function can be obtained using Maple.

Maple Command:

Maple Graph:

Now consider the provided function.

y=x2+lnxx+3

The function is not defined at 0 and âˆ’3 and thus it has two vertical asymptotes as x=0,x=âˆ’3.

Now differentiate the provided function and equate the derivative to zero to obtain the critical points.

f'(x)=12+3x(x+3)

The derivative of the function is not defined at the points0 and âˆ’3 which are not in the domain of the function

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