Chapter 4.3, Problem 44E

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 InExercises 23-56, (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 ) = { 2 x + 1 , x ≤ − 1 x 2 − 2 ,   x > − 1

(a)

To determine

To calculate: The critical points for the provided function f(x)={2x+1        x1x22        x>1}.

Explanation

Given:

The function f(x)={2x+1Â Â Â Â Â Â Â Â xâ‰¤âˆ’1x2âˆ’2Â Â Â Â Â Â Â Â x>âˆ’1}.

Formula used:

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

f'(c)=0

Or the derivative does not exist at c.

Calculation:

It can be seen that the provided function is differentiable on the complete number line

Differentiate the provided function

(b)

To determine

To calculate: The interval where the first provided function f(x)={2x+1        x1x22        x>1} is increasing or decreasing.

(c)

To determine

To calculate: The relative extrema of the function f(x)={2x+1        x1x22        x>1} using the first derivative test.

(d)

To determine

To graph: The function f(x)={2x+1        x1x22        x>1} and find the relative extrema.

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