Question

Given f'(x)=(2-x)(6-x), determine the intervals on which f(x) is increasing or decreasing
Options:
1) Decreasing (-∞,2); increasing on (6,∞)
2) Decreasing (2,6); increasing on (-∞,2)U(6,∞)
3) Decreasing (-∞,2)U(6,∞); increasing on (2,6)
4) Increasing (-∞,-2)U(-6,∞); increasing on (-2,-6)

Answer 1

where is first derivative, f' positive ?
f'(x)=(2-x)(6-x) that is a parabola,
coef of x^2 is + so the vertex is at the bottom
zero when x = 2 and when x = 6 which is
so when x < 2 and when x > 6
so to the left of x = 2 and to the right of x = 6

Answer 2

decreasing between those of course