spent 3 hours trying to figure out this, watched this 8 minutes video -> INSTANTLY KNOW HOW TO DO THE QUESTION... What's my life about? CONSTANT STRUGGLING
This is by far one of the best math explanation videos I've seen on difficult topics! Spent a good time trying to find a way to quickly learn this (wihout knowing what it was called), but only came across hour-long videos that were too convoluted and complicated when I really just needed to learn this for one task. And then I saw your video, and your usage of colors, simple instructions that you go over for each step, your clear explanation with the clear example, all in a short 8-minute long video is just excellent. Thanks a lot 😇⭐
Hikmah Aina fxy always equals fyx, you can make up some functions of x and y and try it for yourself. It’s also true that fxxyy=fxyyx=fyyxx=fyxxy and so on. In this example fxy and fyx just happen to be 1, but in other examples might not be, but they would still be equal.
It’s just a mathematical fact. Try it with any function; they always commute. What I mean is if you did f_xyxxxy (for some function) you can mix up the order of the 4 x’s and 2 y’s and the answer will always be the same.
When you diff Fx wrt y the x term is constant and the diff of y is 1, When you diff Fy wrt x the y term is constant and the diff of x is also 1. F_xy always is equal to F_yx. However they do NOT always equal 1, they just happened to equal to 1 in this example, the mixed derivative F_xy or F_yx could still be a function of y and/or x, such as; F= 3(y^3)(x^4) + e^(-3y) + 2x Fx= 12(y^3)(x^3) +2 Fy= 9(y^2)(x^4) - 3e^(-3y) Fxy= 36(y^2)(x^3) Fyx= 36(y^2)(x^3)
spent 3 hours trying to figure out this, watched this 8 minutes video -> INSTANTLY KNOW HOW TO DO THE QUESTION... What's my life about? CONSTANT STRUGGLING
This is by far one of the best math explanation videos I've seen on difficult topics! Spent a good time trying to find a way to quickly learn this (wihout knowing what it was called), but only came across hour-long videos that were too convoluted and complicated when I really just needed to learn this for one task. And then I saw your video, and your usage of colors, simple instructions that you go over for each step, your clear explanation with the clear example, all in a short 8-minute long video is just excellent. Thanks a lot 😇⭐
bro this was deadset the most helpful math video I've ever watched. THANK YOU!!!
Mate this video has saved my life for my exam tomorrow big thanks
Exemplary explanation, teacher do his vee voo vee vooo in class . After this vdo I actually able to solve 5 equations of homework 👌
what a hero, really clear and easy to follow. wish you were my lecturer haha
you did a fantastic job with my homework! especially now that school is closed because of the corona virus. Thank you so much!!!
Just in 8 minutes.... thanks a lot..... keep it up.
I feel peacefully.... Well explained thanks.
This was really helpful...thank you very much..
I am having exam now, the same exact question is asked and I'm just copying it🌚🌚🌚🙌
Thank you very much for this. However just wanted to know what 'D' stands for
you don't know what the D is? well.... have you ever had a biology class in your school?
D is hessian formula
what if youre fyy is >0 and fxx < 0 what then? what would its nature be?
Can someone please tell me why is (Y = -1/2 x) in the 2 step?
thank u so much bearded scientist!
bro keep up the good work :)
Thank you very much !
Can someone explain for part fxy=fyx=1 ... I don’t get it
Hikmah Aina fxy always equals fyx, you can make up some functions of x and y and try it for yourself. It’s also true that fxxyy=fxyyx=fyyxx=fyxxy and so on. In this example fxy and fyx just happen to be 1, but in other examples might not be, but they would still be equal.
The Bearded Scientist so if :
fx=y+2
fy=1
fxx=2y+x+3
fyy=2
So fxy=fyx equals to...
For examples of your own you need to start with f. For example:
f=2x^2+3xy^4
fx=4x+3y^4
fxy=12y^3
fy=12xy^3
fyx=12y^3
fxy=fyx
Thank you very much.
Great! Thanks a lot!
Hi, What is 'D' stands for?
Thank you so so so much !
extremely helpful! thanks:-)
What happens when D>0 but Fxx and Fyy both = 0
What do you characterise the stationary point in that case?
Hey, D can't be more then 0 if Fxx=0 or Fyy=0
Because D=FxxFyy-Fxy^2
If either equals 0, D=0-Fxy^2
Fxy^2 >=0 as its squared
Which makes D
OH! Sorry didn't think about that - I must have made an error in my working on a sep. question. Thanks a whole bunch :D
No worries.
what if D or fxx are equal to 0?
what if fxx > 0 and fyy < 0 ? is it still a minimum
That can't ever happen, try it yourself for any function.
If Fxx>0, then Fyy>0. If Fxx
Thanks buddy
sorry what i mean exactly is why Fxy=Fyx in the first place??????
It’s just a mathematical fact. Try it with any function; they always commute. What I mean is if you did f_xyxxxy (for some function) you can mix up the order of the 4 x’s and 2 y’s and the answer will always be the same.
What happens when D is zero
what if D=0?
the second derivative test is inconclusive
why does Fxy=Fyx = 1?
When you diff Fx wrt y the x term is constant and the diff of y is 1, When you diff Fy wrt x the y term is constant and the diff of x is also 1.
F_xy always is equal to F_yx. However they do NOT always equal 1, they just happened to equal to 1 in this example, the mixed derivative F_xy or F_yx could still be a function of y and/or x, such as;
F= 3(y^3)(x^4) + e^(-3y) + 2x
Fx= 12(y^3)(x^3) +2
Fy= 9(y^2)(x^4) - 3e^(-3y)
Fxy= 36(y^2)(x^3)
Fyx= 36(y^2)(x^3)
slow it down
why does Fxy=Fyx = 1?
It’s not like that’s always true. It just so happens that it does here.