   Chapter 3.3, Problem 41E

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. C ( x ) = x 1 / 3 ( x + 4 )

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:

Cx=x13x+4

3) Formula:

i. Sum and difference rule:

ddxfx±gx=ddxfx±ddx(gx)

ii. Constant multiple rule:

ddxCfx=Cddx(fx)

iii. Power rule:

ddxxn=nxn-1

4) Calculation:

Consider, Cx=x13x+4

By using rules of exponent

Cx=x43+4x13

Differentiate with respect to x,

C'x=ddxx43+4x13

By using sum and difference rule,

C'x=ddxx43+ddx4x13

By using constant multiple rule and constant function rule,

C'x=d

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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