Find the intervals on which each of the following functions is (a) increasing (b) decreasing.
f(x)=(x-1)(x-2)2=x2-4x+4 * x-1= x3-4x2+4x-x2+4x-4
f(x)=x3-5x2+8x-4
f’(x)=3x2-10x+8
f’(x)=3x2-6x-4x+8
=3x(x-2)-4(x-2)
=(3x-4)(x-2)
Function f(x) is decreasing for x ∈ [4/3,2] and increasing in x ∈ (-∞,4/3) ∪ (2, ∞)