Given the function f (x) = 2ax-x3, a > 0, if f (x) is an increasing function on X ∈ (0,1], find the value range of A

Given the function f (x) = 2ax-x3, a > 0, if f (x) is an increasing function on X ∈ (0,1], find the value range of A

∵ f (x) is an increasing function on X ∈ (0,1], ∵ f '(x) = 2a-3x2 is positive on (0,1], ∵ 2A > 3x2 is constant, that is, a > 32X2, ∵ x ∈ (0,1], ∵ 32X2 ∈ (0,32], ∵ a > 32, and a = 32, ∵ a ≥ 32