The maximum value of function f (x) = x (1-x ^ 2) on [0,1] is? The maximum value of function y = X-2 √ X in [0,4] is? The following four propositions are given ① The function y = x ^ 2-5x + 4 (- 1 ≤ x ≤ 1) has a maximum value of 10 and a minimum value of - 9 / 4 ② The function y = 2x ^ 2-4x + 1 (2 < x < 4) has a maximum value of 17 and a minimum value of 1 ③ The maximum value of function y = x ^ 3-12x (- 3 ≤ x ≤ 3) is 16, and the minimum value is - 16 ④ The function y = x ^ 3-12x (- 2 < x < 2) has no maximum or minimum

The maximum value of function f (x) = x (1-x ^ 2) on [0,1] is? The maximum value of function y = X-2 √ X in [0,4] is? The following four propositions are given ① The function y = x ^ 2-5x + 4 (- 1 ≤ x ≤ 1) has a maximum value of 10 and a minimum value of - 9 / 4 ② The function y = 2x ^ 2-4x + 1 (2 < x < 4) has a maximum value of 17 and a minimum value of 1 ③ The maximum value of function y = x ^ 3-12x (- 3 ≤ x ≤ 3) is 16, and the minimum value is - 16 ④ The function y = x ^ 3-12x (- 2 < x < 2) has no maximum or minimum

The first question: F '(x) = 1-3x ^ 2, Let f' (x) = 0, x = 1 / √ 3 or x = - 1 / √ 3. Therefore, if f (x) increases on [0,1 / √ 3], and decreases on [1 / √ 3,1], the maximum value is obtained at x = 1 / √ 3, and the maximum value is 2 √ 3 / 9. The second question: let t = √ x (the value range of T is [0,2]), then y = T ^ 2-2t = (t-1) ^ 2-1