   Chapter 4.4, Problem 52E Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Solutions

Chapter
Section Calculus: Early Transcendental Fun...

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

Using the Second Derivative Test InExercises 37-58, find all relative extrema of the function. Use the Second Derivative Test where applicable. g ( x ) = 1 2 π e − ( x − 3 ) 2 / 2

To determine

To calculate: The relative extrema of the provided function f(x)=12πe(x3)22 using the second derivative test.

Explanation

Given:

The function f(x)=12πe(x3)22

Formula used:

For a function f that is twice differentiable on an open interval I,

If f'(c)=0 for some c, and,

If f''(c)>0 the function f has relative minima at c

If f''(c)<0 the function f has relative maxima at c.

If f''(c)=0, the test fails.

Calculation:

First differentiate the provided function,

f'(x)=(x3)2πe(x3)22

Equate the first derivative to zero to obtain the critical points.

(x3)2πe(x3)22=0x3=0x=3

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