Points of inflections are zeroes of the second derivative. We have:
[tex]f(x)=x^3-6x^2+12x\implies f'(x)=3x^2-12x\implies f''(x)=6x-12[/tex]
So, the second derivative equals zero if and only if
[tex]f''(x)=0\iff 6x-12=0 \iff 6x=12 \iff x=2[/tex]
So, this is the only point of inflection of this function.
