Find and Classify all Critical Points of a Multivariable Function
Find critical points by solving for all points that make the first partial 0. Classify those critical points using the Hessian matrix.
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Пікірлер: 36
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@NakiaRimmer
Жыл бұрын
That encouraging! Thank you
@diptendu88
6 ай бұрын
000p@@NakiaRimmer
This video is amazing! The energy and your explanations is unmatched on youtube! Thank you
thank you for the video, i love that you were not doing unnecessary easy computation, but went straight to the point and saved my time. i liked the video
finally a video that’s actually helpful, i watched tons and all of them solved pretty simple questions
You are saving me for this final. Thank you so so much! Amazing explanation
Really nice video thanks Nakia!
This was great. It really helped me.
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@NakiaRimmer
Жыл бұрын
Thank you so much 😀
excellent problem has max, min and saddle points!!!!
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Can you help please how classification of critical points of system in three equation in 3d
@thirsty3852
Жыл бұрын
عساك عرفت
How to know 3:06 ? Like how did you get y=0 or y=2?
@NakiaRimmer
3 жыл бұрын
I should have been more clear, I am setting the expression 3y(y-2) equal to zero since critical points occur when the first partial derivatives are zero simultaneously.
Hi and thanks a lot for your help! My problem is the following: I would like to draw a phase diagram for a system of 3 differential equations And it has three parameters
what happened to 3x^2 when you moved to 3y^2-6y
@NakiaRimmer
3 жыл бұрын
That was under the case where x = 0
Why is it that when you analyze the sign of D(x,y) and it becomes >0, that you always analyze fxx. Why not fyy or fxy or even f(x,y). What's the reason for this?
@NakiaRimmer
Жыл бұрын
Great question! I’m going to throw out a bunch of terms and give you a link to a video. If that video doesn’t do it for you, then throw the terms into the search and hopefully you can find a better one.
@NakiaRimmer
Жыл бұрын
For a function f(x,y), there is a matrix made up of the second partial derivatives. That matrix is called the Hessian. The determinant of this matrix along with the eigenvalues of the matrix are used to classify critical points.
@NakiaRimmer
Жыл бұрын
The determining factor that distinguishes a local max from a local min is the calculation of whether the matrix is positive definite or negative definite. Checking the sign of f_xx is a shortcut to this calculation.
@NakiaRimmer
Жыл бұрын
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Thank you! Great explanation
Waaaaw amazing teacher 😊