Is there a mistake?

$\displaystyle y=x^3-6x^2+9x$

$\displaystyle y'=3x^2-12x+9$

$\displaystyle y'=0$

$\displaystyle x=3 and x=1$

Extreme local:

P(1,4) ---> Point maximum

P(3,0) ---> Point minimum

$\displaystyle y''=6x-12$

Point of inflection:

P(2,2)

Sorry. Is there any way to put graphic here?