If f (x) = x ^ 3-x ^ 2-x + 1, what is the maximum value of X on [- 1,1]?

If f (x) = x ^ 3-x ^ 2-x + 1, what is the maximum value of X on [- 1,1]?

f(x)=x^3-x^2-x+1
f'(x)=3x^2-2x-1=(3x+1)(x-1)
When x < - 1 / 3, it increases monotonically
When - 1 / 3 < x < 1, monotonically decreasing
In the interval [- 1,1], there is a maximum when x = - 1 / 3
f(-1/3)=(-1/3)^3-(-1/3)^2-(-1/3)+1=32/27