Given that the function g (x) = 1 / 3ax ˇ 3 + 2x ˇ 2-2x, the function f (x) is the derivative of the function g (x) When a ∈ (0, + ∞), if there is a negative number m related to a, such that - 4 ≤ f (x) ≤ 4 is constant for any x ∈ [M, 0], the minimum value of M and the corresponding value of a are obtained

Given that the function g (x) = 1 / 3ax ˇ 3 + 2x ˇ 2-2x, the function f (x) is the derivative of the function g (x) When a ∈ (0, + ∞), if there is a negative number m related to a, such that - 4 ≤ f (x) ≤ 4 is constant for any x ∈ [M, 0], the minimum value of M and the corresponding value of a are obtained

f(x)=ax^2+4x-2.
If we want to minimize m, that is to say, if we want to minimize x 1 of | f (x) | = 4, the further away from the origin, the negative value
Draw the figure of F (x). The axis of symmetry is x = - 2 / A. at x = 0, f (x) = - 2;
In X ∈ [M, 0], we can obtain that X has only two places, the axis of symmetry and x 1
1, if x = - 2 / A, | f (x) | > 4,
That is 4 / A + 2 > 4, a