13: Second Partial Derivative Test Derivation - Valuable Vector Calculus

[@txikitofandango]

The summary at the end was crucial for me. Thanks! It's amazing you were able to talk about a function of two variables without drawing a 3D graph.

[@kiiometric]

I see the Hessian hidden at the end, very sneaky

[@physicist2337]

Great video, man! I remember not conceptually understanding this in calc 3, and I felt as though I was cheating a bit by just brainlessly computing with this test. Great to see the intuition.

[@superuser8636]

Hey, thanks for the discriminant and quadratic tip and insight. It makes total sense. I think I’ve just always used the determinant instead with the same result. Let me know what you think, I can define the operation if you need. Nice video

[@iyadindia862]

At 8:03 As you have said that here is slope in y direction as you move along dx Is there a chance for slope in x direction when u move little bit along dy Pls make clarify

[@MuPrimeMath]

Yes, moving in the y direction affects the slope in the x direction. However, because y is zero while we integrate along x, it doesn't affect the result!

[@medchs]

how can one explain this asymmetry?

[@MuPrimeMath]

The asymmetry is just a result of the path that I chose for this video, where we start by moving in the x direction. If we instead started in the y direction, it would be the opposite. However, because mixed partials are equal for smooth functions, the final answer is the same both ways!

[@medchs]

@@MuPrimeMath Thank you so much! I get it now.👍

[@iyadindia862]

We expect your vedios on multiple integrals and the way one has to visualise,vector integration and theorems like stokes,Guass's and divergence theorem in coming days.

[@elektikplayz129]

amazing explanation

[@abraramin3146]

Can you make a video on Newton Leibnitz theorem

[@MuPrimeMath]

If you're referring to the fundamental theorem of calculus, 3blue1brown has some good videos on that, so you can check out some of his calculus videos!

[@ZackSussmanMusic]

Thank you for the amazing content!

[@anis_coc6227]

تا شييكووور

[@alejrandom6592]

now I understand pringles. Jk, this is really beautiful stuff!

[@sergiomanzetti1021]

Nice, but I noticed, why do Americans say "poeee" and not "pɔɪnt" for the work "point". Almost, can hear "poaaee" instead of "pɔɪnt". It sounds "cute", but is it correct pronounciation?