   Chapter 3.3, Problem 33E

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 ) = x 3 − 12 x + 2

To determine

(a)

To find:

The intervals of increase or decrease

Explanation

1) Concept:

By using Increasing or decreasing test

2) Test:

Increasing or Decreasing test:

If f'x>0 then f is increasing

If f'x<0 then f is decreasing

3) Given:

fx=x3-12x+2

4) Formula:

i. Sum and difference rule:

ddxfx±gx=ddxfx±ddx(gx)

ii. Constant function rule:

ddxC=0

iii. Constant multiple rule:

ddxCfx=Cddx(fx)

iv. Power rule:

ddxxn=nxn-1

5) Calculation:

Consider, fx=x3-12x+2

Differentiate with respect to x,

f'x=ddx(x3-12x+2)

By using sum and difference rule,

f'x=ddx(x3)-ddx(12x)+ddx(2&

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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