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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
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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