Find the value(s) of x for which y=[x(x-2)]^2 is an increasing function.

f(x)=[x(x-2)]^2
We know for increasing function we have f'(x)≥0
Therefore, f'(x)=2[x(x-2)][d/dx(x-2)]
or, f'(x)=2[x(x-2)][d/dx(x^2-2x)]=2x(x-2)(2x-2)
=4x(x-2)(x-1)
For f'(x)≥0, i.e., 4x(x-1)(x-2)≥0
The values of x are: x∈[0,1]∪[2,∞).