I have a calculus test tomorrow on curve sketching. I have to know how to find the asymptotes, max/min pts, pt of inflection and then sketch it...

Im having abit of trouble with max/min pts. I'd really appreciate it if anyone could help me with this.

Lets do a short example. Say x^4 - 8x^3 + 18x^2..

so the first step would be to find dy/dx

dy/dx = 4x^3 - 24x^2 + 36x

= 4x(x^2 - 6x +9)

=4x(x - 3) ^2

Set dy/dx = 0

0 = 4x(x - 3) ^2

x = 0

x = 3

Now this is where im stuck at.. what would be my next step?

(Note: Also i have seen some questions being solved by finding the second derivative... Could you also explain to me which should be used, first or second derivative, when it comes to determining the max/min pts)

Thank you so much for any help you guys would provide ^_^