Talk:Second derivative test

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[edit] Functions of Two Variables

This article should be expanded to include functions of more than one variable, e.g. f(x,y) = x^4 + y^4 -4xy + 1. I will probably come back to this page later and fix this when I have time (in a week or two?), but if anyone wants to do it before me, feel free. Eck

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What about the inflection point when the second derivative is zero?

Exactly, also accordig to http://mathworld.wolfram.com/InflectionPoint.html .

[edit] Consider this..

What about [ f(x):=x^2, f2(x):=2 ]? Consider [ x0:=3, r:=1 ]. [ f2(x) ] is continuous on [ x = 2..4 ] and [ f2(3)>0 ], but [ f(x0) ] is NOT a minimum of [ f(x) ]. - 149.159.92.56

x0=3 is not a critical point (the derivative there is 2x=6, not 0). —Steven G. Johnson 04:30, Jan 5, 2005 (UTC)