   Chapter 3.3, Problem 10E

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 ) = 2 x 3 − 9 x 2 + 12 x − 3

To determine

(a)

To find:

The intervals on which f(x)  is increasing or decreasing

Explanation

1) Concept:

The derivative of a function may 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=2x3-9x2+12x-3

f'x=6x2-18x+12=6x2-3x+2=6(x-1)(x-2)

6x-1x-2=0 x=1 and x=2

The critical points are x=1 and x=2

Intervals are -,1, <

To determine

(b)

To Find:

Local maximum and local minimum value of f(x)

To determine

(c)

To find:

Intervals of concavity and inflection points

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