Maths the intervals function

f = 2x^3 - 9x^2 + 12x
f ' = 6x^2 - 18x + 12 = 6(x^2 - 3x + 2) = 6(x- 2)(x - 1)
Put f ' = 0, x = 1 or 2.
f " = 12x - 18 = 6(2x - 3)
When x = 1, f " < 0, so x = 1 is a max.
When x = 2, f " > 0, so x = 2 is a min.
Interval where f(x) is increasing are : x < 1 and x > 2.
Interval where f(x) is decreasing is : 1 < x < 2.