   Chapter 3.3, Problem 39E

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 6 − x

To determine

a)

To find:

The intervals of increase or decrease

Explanation

1) Concept:

Increasing or Decreasing test:

If f'x>0 then f is increasing

If f'x<0 then f is decreasing

2) Given:

Fx=x 6-x

3) Formula:

i. product rule:

ddxfx.gx=gxddxfx+f(x)ddx(gx)

ii. Constant multiple rule:

ddxCfx=Cddx(fx)

iii. Power rule:

ddxxn=nxn-1

4) Calculation:

Consider, Fx=x 6-x

By using rules of exponent,

Fx=x 6-x12

Differentiate with respect to x,

F'x=ddxx 6-x12

By using product rule,

F'x=xddx6-x12-6-x12ddxx

By using power rule,

F'x=x·

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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