Finding the extrema of functions.

[EgzonKorenica]

I don't have problem finding extremas of a function, I just have one single problem on discussing it. I'm talking about the case when D(x,y)=0, in this video I watched it says inconclusive (honestly in this case I don't know what it means), meanwhile in my math books it says that in this case there should be more "investigation", meaning that the second derivative wasn't enough to determine whether the function has an extrema. So, what I saw in my book is that they substitute D(x,y) with delta (triangle) and make something up which I don't really understand.

And the question is, could someone explain what to do in case when D(x,y)=0?

p.s sorry for exagerrating.

 

[stapel]

Remember when you learned about solving systems of linear equations using determinants, and you learned that, if certain determinants evaluated to zero, you couldn't say if the underlying system had "no solution" or "infinitely-many solutions"? And you had to "do further investigations" to figure out which it was?

I think you're dealing with something similar here. It's a test which can give lots of info, but, in certain cases, doesn't give you quite enough. That's all in the world they mean.