Maximum and minimum value of the function f(x)=1/2x^3-x^2
on the interval: -1 ≤x ≤1
I am going to assume you mean (1/2)x^3- x^2 just because it is simplest. Your notation is still ambiguous.
Now, what have you learned about this? Do you know this theorem: "A function takes on it maximum and minimum values on an interval in one these places:
1) at the endpoints of the interval
2) where the derivative does not exist
3) where the derivative is 0.
If I have the right function, it is a polynomial and its derivative always exists. Can you find the derivative?