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Reference to Second partial derivative test should be deleted

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The article on the second partial derivative test is pretty poor. In particular, the only case which is discussed in any detail is a function of two variables. I added a few sentences to the article pointing out that the eigenvalues of the Hessian are, in the general case, the quantities of interest, but there's no information on that page (e.g. a proof) that does not already appear on this page. —Preceding unsigned comment added by 141.211.98.79 (talk) 14:56, 29 January 2009 (UTC)[reply]

Functions of Two Variables

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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

Inflection points

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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 .
is a necessary, but not a sufficient, condition for an inflection point. Oli Filth 18:50, 15 May 2007 (UTC)[reply]

Consider this..

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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)

Third derivative?

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I could not understand what to do when the second derivative is zero. What am I to do with the third derivative? Could someone describe this better? —Preceding unsigned comment added by 129.177.17.70 (talk) 06:31, 27 November 2009 (UTC)[reply]

Revamp

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I revamped the article. It was a mess, full of accumulated errors, the most serious of which confused concavity and extrema. Some more work could be done but I have to say I don't really care enough to do it. I just didn't want gross inaccuracies on a site some of my calc students might visit. 50.132.8.186 (talk) 06:19, 18 April 2013 (UTC)[reply]