   Chapter 3.3, Problem 11E

Chapter
Section
Textbook Problem

# 9-14(a) Find the intervals on which f is increasing or decreasing.(b) Find the local maximum and minimum values of f.(c) Find the intervals of concavity and the inflection points. f ( x ) = x 4 − 2 x 2 + 3

To determine

(a)

To find:

The intervals on which f  is increasing or decreasing

Explanation

1) Concept:

The derivative of a function can be used to determine whether the function is increasing or decreasing on any intervals in its domain.

If f'x>0  over an interval I,  then fx is increasing on I.

If f'x<0  over an interval I, then fx is decreasing on I.

2) Calculation:

fx=x4-2x2+3

f'x=4x3-4x=4xx2-1

Set f'x=0

4xx2-1=0

4x=0x=0

x2-1=x+1x-1=0x=-1, x=1

The critical points are x=-1, x=0 and x=1

Intervals are -,-1, -1, 0 ,0, 1 and

To determine

(b)

To find:

Local maximum and local minimum values of f(x)

To determine

(c)

To find:

Intervals of concavity and inflection points

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