# Classifying points found with derivative

I've been trying to learn derivatives recently. I have troubles with finding local minimums and maximums given an equation

I have understood this far

$$y=2x^3-9x^2+12x-5$$

$$dy/dx= 6x^2-18x+12$$

$$x=1$$ or $$x=2$$

$$f(1)=0$$
Point A $$(1,0)$$

$$f(2)=-1$$
Point A $$(2,-1)$$

What I do not understand is how one categorizes the points, either as minimums or maximums. I have looked around but I can't make sense of the explanations.

• ${d^2 y \over d x^2} > 0:$ local minimum
• ${d^2 y \over d x^2} < 0:$ local maximum
• ${d^2 y \over d x^2} = 0:$ point of inflection