Question

find the extreme values of f(x)=2x^3-9x^2+12x on [0,3] and [0,2]

Answer 1

I'm not sure, but here's my guess. Take the derivative of this f(x)
6x^2 - 18x + 12 = x^2 - 3x + 2
(x -1) (x - 2) = 0 ( critical points)
x =1, x = 2
1,2 are within the closed interval.
here i'm stuck, but I think you will have to evaluate f(0) and f(3) to get the max value and min value of the closed interval [0, 3]. Then f(0) and f(2) to get the max and min value of the [0, 2] interval. I'm not 100% sure it's correct, just my opinion. Cheers.