2nd Derivative Test conquered?

[prasannapakkiam]

Okay, I have made up this rule. I would love to call it mine, but I am sure some one is bound to have invented it by now...

f(x)
find a such that f '(a)=0
now find the first nth derivative such that f^n(a) !=0
Usually n=2.

1. If n E odd - Inflexion, If n E even, keep going...
2. If f^n(a)>0 - Minima, If f^n(a)<0 - Maxima.

Well that is the jist of it...
Is it valid?

 

[lalbatros]

Yes, obvious, if you visualise the function from its Taylor series expansion:

f(x) = (x-a)^n f^n(a)/n! + ...