Consider the following function.

f(x) = x4 – 8×3 + 18×2 + 8

(a) Make a sign diagram for the first derivative.

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X

f'(x) gt;0

X=

f’ (x) lt;0

f ‘ (x) =0

(b) Make a sign diagram for the second derivative.

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X =

X =

(c) Sketch the graph, showing all relative extreme points and inflection points.

y

401

IP

IP

IP

20/

IP

-4

– X

-2

2

– X

4

-4

-2

2

4

-20

-20

O

-40-

O

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