critical and inflection points

[sabenada]

I need to find the maximums, minimums, and points of inflection of the following equation:

2x^5-8x^4+7x^3-10x^2+10x-5

HOW? :idea:

 

[tkhunny]

Guessing?
Magic?
First and Second Derivative Tests?
Acid Etching?

Come on, give us SOMETHING to work with!