Answer:
f(x) = 2x3 ? 3x2
? 36x + 7
f?(x) = 6x2
? 6x ? 36
= 6(x2
? x ? 6)
= 6 (x ? 3) (x +
2)
f?(x) = 0 x = ?2, 3
Intervals are :
when then f?(x)
= 6 (?)(?) > 0
when then f?(x)
= 6 (?)(+) < 0
when then f?(x)
= 6 (+)(+) > 0
(a) f(x) is strictly
increasing in
(b) f(x) is strictly
decreasing in (?2, 3).
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