Answer:
We have, f(x)= x
3
−12x
2
+36x+17
⟹f(x)=3x
2
−24x+36=3(x−6)(x−2)
a. For f(x) to be increasing, we must have
f
′
(x)>0
⟹3(x−6)(x−2)>0
⟹x<2orx>6
⟹xϵ(−∞,2)∪(6,∞)
So, f(x) is increasing on (−∞,2)∪(6,∞)
b. For f(x) to be decreasing, we must have
f
′
(x)<0
⟹3(x−2)(x−6)<0
⟹2<x<6
So, f(x) is decreasing on (2,6)
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