   Chapter 3.3, Problem 35E

Chapter
Section
Textbook Problem

# 33-44(a) Find the intervals of increase or decrease.(b) Find the local maximum and minimum values.(c) Find the intervals of concavity and the inflection points.(d) Use the information from parts ( a ) − ( c ) to sketch the graph. Check your work with a graphing device if you have one. f ( x ) = 1 2 x 4 − 4 x 2 + 3

To determine

To find:

The intervals of increase or decrease

Explanation

1) Concept:

By using Increasing or decreasing test

2) Test:

Increasing or Decreasing test:

i. If f'x>0 then f is increasing

ii. If f'x<0 then f is decreasing

3) Given:

fx=12x4-4x2+3

4) Formula:

i. Sum and difference rule:

ddxfx±gx=ddxfx±ddx(gx)

ii. Constant multiple rule:

ddxCfx=Cddx(fx)

iii. Power rule:

ddxxn=nxn-1

5) Calculation:

Consider, fx=12x4-4x2+3

Differentiate with respect to x,

f'x=ddx12x4-4x2+3

By using sum and difference rule,

f'x=ddx12x4-ddx4x2+ddx(3)

By using constant multiple rule and constant function rule,

f'x=12ddxx4-4ddxx2+0

By using power rule,

f'</

To determine

(b)

To find:

Local maximum and local minimum values

To determine

(c)

To find:

Intervals of concavity and the inflection points

To determine

(d)

To sketch:

The graph by using information from part (a) – (c)

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