   Chapter 3.3, Problem 36E

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. g ( x ) = 200 + 8 x 3 + x 4

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:

gx=200+8x3+x4

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, gx=200+8x3+x4

Differentiate with respect to x,

g'x=ddx(200+8x3+x4)

By using sum rule,

g'x=ddx200+ddx8x3+ddx(x4)

By using constant function rule and constant multiple rule,

g'x=0+8ddxx3

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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