Find the intervals on which each of the following functions is (a) increasing (b) decreasing.
f(x)=x3-12x2+36x+17
f’(x)=3x2-24x+36
f’(x)=3(x2-8x+12)
=3(x-6)(x-2)
Function f(x) is decreasing for x ∈ [2,6] and increasing in x ∈ (-∞,2) ∪ (6, ∞)