   Chapter 3.3, Problem 38E

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. h ( x ) = 5 x 3 − 3 x 5

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:

hx=5x3-3x5

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, hx=5x3-3x5

Differentiate with respect to x,

h'x=ddx5x3-3x5

By using sum and difference rule,

h'x=ddx5x3-ddx3x5

By using constant multiple rule and constant function rule,

h'x=5ddxx3-3ddxx5

By using power rule,

h

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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