Given the real number a ≠ 0, the function f (x) = ax (X-2) ^ 2 (x belongs to R) (1). If the function f (x) has the maximum value 32 | 27, find the value of A (2) If the inequality f (x) < 32 holds for any x, the value range of a is obtained

Given the real number a ≠ 0, the function f (x) = ax (X-2) ^ 2 (x belongs to R) (1). If the function f (x) has the maximum value 32 | 27, find the value of A (2) If the inequality f (x) < 32 holds for any x, the value range of a is obtained

(1) If the derivative of F (x) is a (3x ^ 2-8x + 4), let this derivative be zero, then we can get x = 2 / 3 or x = 2, that is to say, we can only get the extremum at x = 2 or x = 2 / 3. Obviously, f (2) = 0, so f (2 / 3) = 32 / 27, so a = 1 (2) can be obtained from (1), and f (x) has a polar point 2 / 3 at [- 2,1], so if