Hello. I am just wondering about how to start this problem: Prove the Second Partials Test. The book I am using gives a hint of: Compute the directional derivative of(adsbygoogle = window.adsbygoogle || []).push({}); fin the direction of the unit vectoru= hi+ kjand complete the square.

I guess I am just having trouble even starting it. Am I supposed to define f or something of that nature to start? I just cannot see how to take the derivative offwithout knowing whatfis. Thanks.

edit... Well I thought about it, and I guess I could say that the directional derivative is [tex]f_x h + f_y k[/tex]

But completing the square there? Do I need to take the directional derivative again? [tex](f_{xx} h + f_{yx} k)h + (f_{xy} h + f_{yy} k)k[/tex] Then complete the square?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Proving the Second Partials Test

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**