Second partial derivative test

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How to determine if the critical point of a two-variable function is a local minimum, a local maximum, or a saddle point.

[@abaundwal]

This man is a lifesaver. I'm almost in tears. :')

[@rahuldutta9303]

interesting surname u got there sir.just a rearrangement of one letter and we will get something even more interesting,no offense tho

[@mohitpandey4655]

@@rahuldutta9303 oooh bhai 😂😂😂😂

[@RSA_Shock]

You and Sal khan need to get the noble peace prize for the amount of good you have done for the world

[@ayushsingh-ib9nu]

Using a graph really helps. Thanks for the efforts

[@jvcmarc]

isn't that test formula the determinant of the Hessian matrix

[@TheLeontheking]

scrolled to the comments to look for such a comment.. great how it all comes together!

[@anonymous_4276]

Hessian is the analogue of the second derivative for a function with multiple inputs and one output. The gradient is the analogue of the first derivative in this case. Move along any direction [dX]=[dx,dy], the change in function value will be gradient.[dx,dy] (dot product of gradient with [dx,dy]. Similarly, the change in this change (of the output) as we move along [dx,dy] will [dX(transpose)][Hessian][dX] (here we are doing matrix multiplication). That is basically the reason that formula shows up.

[@leytonzhang5607]

wow that is so freakin intuitive.. Grant. You are nutz.

[@Ryannocerous]

Great job, Very intuitive.

[@niharikatasnim939]

But why are we subtracting fxy^2? What's the significance of this term? What does it mean geometrically?

[@SohamChakraborty42069]

Isn't that the Hessian determinant in expanded form?

[@Ben-dm8fi]

Yes it’s the determinant of the hessian matrix of the second partial derivatives. Easier to explain like this bc many people don’t know the hessian at this point in their math careers

[@snehamoypatra9786]

Why scientist always hide the beauty. let make mathematics understandable for all people. what a amazing teacher you are

[@a.fleischbender7681]

Love you Grant

[@Chino50863486]

what should we do when we get the special case of 0?

[@debjyotichattopadhyay6679]

Really nice ....deserve more views

[@ahmedezzat687]

are you the guy of "3brown 1blue" ? anyway you have explained it very well, thank you

[@elgatito00]

Math God❣️

[@kas8131]

I’m watching this series just for fun

[@stickAran]

6:52 MISTAKE DETECTED. its supposed to be fxy(xo,yo)^2 -fxx(xo,yo)*fyy(xo,yo)

[@ponderingprachiti]

eureka! it is the determinant of the Hessian matrix!

[@hari8568]

Why does this seem like sorcery to me :(

[@TheLeontheking]

start with 3b1b's videos on single-variable-calculus, then start from the beginning of this series, take notes, and it will start to make sense for you :)
Also i find pausing a video regularly, and reflecting on the steps taken, as well as which steps might lay ahead, very useful!

[@vladimirtomin8223]

Without watching next video I will try to guess: when green part of the formula is bigger than red part of the formula it basically means that both half are in agreement and compliment direction of one another by multiplication

[@shwetupadhyay4822]

legend!!!!!!

[@wkdwoals]

I love you Grant

[@ramiz2999]

Thank you for the video. I have a question: why ∂/∂x ( ∂z/dx) isn't ∂^2z/d^2x^2) or why ∂x (∂x) is ∂x^2 and not ∂^2x^2?

[@fahrenheit2101]

Its just notation really

[@Goku17yen]

Graph looks like -x^2, if using both complex and Cartesian plane lmao

[@JM-fo1te]

:( too many mistakes.

[@jacobraji2442]

what mistakes are you referring too?

[@kaazflip3961]

Nerd

[@elgatito00]

Math God❣️