Find the extremum and maximum value of function y = x ^ 3-x ^ 2-x + 1 in X belonging to [- 2,2]

Find the extremum and maximum value of function y = x ^ 3-x ^ 2-x + 1 in X belonging to [- 2,2]

Let the derivative of the function 3x ^ 2-2x-1 = 0, and get x = 1 or - 1 / 3, then it is easy to get that x = 1 or - 1 / 3 is the extreme point of the function, when x = 1, it is the minimum value, y = 0; when x = - 1 / 3, it is the maximum value, y = 32 / 27; when x = 2, y = 3 is the maximum value, when x = - 2, it is the minimum value, y = - 9
The overall function image trend is increasing at (- 2, - 1 / 3), decreasing at (- 1 / 3,1), and increasing at (1,2)