Given f '(x) = (2 - x)(6 - x), determine the intervals on which f(x) is increasing or decreasing

Answer 1

d/dx [ (2-x)(6-x) ] = slope of f'(x), where is it + ?
= (2-x)(-1) + (6-x)(-1)
= -2+x -6 + x = 2 x-8
that is + if x >4
and it is - if x<4

Answer 2

f'(x) is negative between the roots of 2,6 and positive otherwise.
So, f is increasing on (2,6) and decreasing elsewhere.