Chapter 4, Problem 37RE

### 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

# Applying the First Derivative Test In Exercises 29-38,(a) find the critical numbers of f, if any, (b) find the open intervals on which the function is increasing or decreasing,(c) apply the First Derivative Test to identify all relative extrema, and (d) use a graphing utility to confirm your results. f ( x ) = ln x − x 2

(a)

To determine

To calculate: The critical points for the provided function f(x)=lnxx2.

Explanation

Given:

The function f(x)=lnxâˆ’x2.

Formula used:

The function f said to have a critical point at c if:

f'(c)=0

Calculation:

It can be seen that the provided function is differentiable on the positive real number line.

Differentiate the provided function.

f'(x)=1xâˆ’2x

Equate this to zero and then solve for x to obtain:

<

(b)

To determine

To calculate: The interval where the first provided function f(x)=lnxx2 is increasing or decreasing.

(c)

To determine

To calculate: The relative extrema of the function f(x)=lnxx2 using the first derivative test.

(d)

To determine

To graph: The function f(x)=lnxx2 and calculate the relative extrema.

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