Chapter 4, Problem 90RE

### 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 In Exercises 81-92, analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. f ( x ) = ln ( x 2 − 3 )

To determine

To graph: The function f(x)=ln(x23).

Explanation

Graph:

Consider the provided function. The argument of the logarithmic function needs to positive. Thus the domain of the function is (âˆ’âˆž,âˆ’3),(3,âˆž).

The logarithmic function has no restriction on it output value. Thus, the range of the function would be (âˆ’âˆž,âˆž).

Now find the x and y intercepts by equating f(x) and x to zero respectively to obtain:

The function has two x-intercept as (2,0),(âˆ’2,0) and no y-intercept.

Now, differentiate the function with respect to x and equate it to zero to obtain the critical points.

2xx2âˆ’3=02x=0x=0

This point does not lie in the domain of the function and thus the function does not have any critical points or extremas.

Now equate the second derivative to zero to get the inflection points

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