Given that a > 1, the function f (x) = the third power of X - ax is a monotone increasing function on [1, + infinity), then the maximum value of a is?

Given that a > 1, the function f (x) = the third power of X - ax is a monotone increasing function on [1, + infinity), then the maximum value of a is?

f(x)=x^3-ax
We get f '(x) = 3x * x-a
Monotone increasing function of function f (x) on [1, + infinity]
Then, 3x * x-a > = 0 holds on [1, + infinity)
So a