I have few questions about extrema of fonctions of two variables. It is written in my textbook: "At a local maximum, the gradient vector must be nul or undefined. A similar reasoning shows that the gradient must be nul at a local minimum." Actually there was no preceeding reasoning to this statement so I don't understand.(adsbygoogle = window.adsbygoogle || []).push({});

- Why couldn't the gradient vector be undefined at the min?

- If one of the partial derivative is undefined at a certain point, does it automatically means the point is a max? If no, how do you tell analytically?

- If (a,b) is a critical point because the gradient at (a,b) is 0 and if the test of the second order partial derivative fails (i.e. =0). How can I conclude analytically to the nature of the critial point?

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# 2 var critical point questions

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