3:58 I think this is incorrect, this would make every point a saddle point unless it is a global optimum, as when you take as a neighbourhood the entire space there will be points of which the image is lower and points of which the image is higher. I think that for a saddle point you should look at α and β separately.
I should have said that a differentiable function f which has a critical point (a,b) is said to be saddle point if that condition is satisfied.. Thanks for pointing it out..👏👏
f(x,y) = 2x^3 + 2y^3 - 9x^2 + 3y^2 + 12y When I calculated fx=0 and fy=0 separately for critical points I got x=0 and x=3,y=1 and y=-2 so should I consider (0,1),(0,3),(3,1),(3,-2)?
3:58 I think this is incorrect, this would make every point a saddle point unless it is a global optimum, as when you take as a neighbourhood the entire space there will be points of which the image is lower and points of which the image is higher. I think that for a saddle point you should look at α and β separately.
I should have said that a differentiable function f which has a critical point (a,b) is said to be saddle point if that condition is satisfied..
Thanks for pointing it out..👏👏
Thank you so much, I enjoyed every minute of your lecture
Welcome and happy to hear that 😊
amazing content sir please keep helping us
and also come back to coep
Thank you.. Happy to hear that videos r still helping to you all..
Coming back😐!! It's difficult ☹️ future ka pata nai, anything can happen
@@DrMathaholic 🥺
Phenomenal explanation. Thank you!
Thank you 😊
Heartly congratulations sir ji...🎊🎉
1k subscribe milestone complete before 1 day of ESE
Thank you Abhay😊
Thankyou so much sir ❤❤❤
Sir, kindly make an video on quadratic forms
Sure.. I will try soon..
Thank you sir ❤
@@kamrulhassan7157 welcome 😊
Thank you so much Sir!! All the videos were very helpful ! When will we be seeing the video on Langrange's multipliers?
Welcome.
Glad to hear that..
About Lagrange multipliers,its late now.. Nobody asked me before and now I am on Diwali vacation till 17th.
1) Critical point (-3,3) - local minima 2) Critical point (-1/2,-1,3/2) - local minima
Thank you Madhavi for posting the answer.. appreciated!!
Sir, is saddle point same as point of inflection?
Wish the bests for you
Thank you 😊
Thank you from iraq
Thank you for your wishes and welcome 😊
Thank you so much sir ☺️
Welcome:)
Awesome video! Thank you!
Welcome:)
YOU ARE GENIOUS
@abedulkareemqasim9441 thank you for your kind words 😊
Explained Well. Thanks.
Glad to hear that.. thank you :)
Really nice sir ji
Thank you Vishnu.😀
Hope you r doing well 😀
Sir, please can you upload a video on Langrange's multipliers?
Its bit late to ask dude.
I am at my home for Diwali..
So next video, may be after 18th..
where you got the x^4 from??
At what timestamp ??
Very good explanation.
One comment: while finding the Hessian matrix of the example I think the hand was directed to incorrect matrix term. Thank you
Thank you..
Oh okay..
Thanks for pointing it out..
Sir, if delta1 is zero, what we get? Can you explain for me? Thank you.
Then the test fails we cannot conclude..
Thank you sir.
Welcome 🙂🙂
dude you saved me
Welcome 😀
Thank you.
Welcome 😀
I was looking for a proof for this - maybe just the 2D case for starters. Anyone has a reference?
See book by Thomas calculus
f(x,y) = 2x^3 + 2y^3 - 9x^2 + 3y^2 + 12y
When I calculated fx=0 and fy=0 separately for critical points I got x=0 and x=3,y=1 and y=-2 so should I consider (0,1),(0,3),(3,1),(3,-2)?
For safer side, check whether these 4 (x,y) points satisfy fx and fy or not..
@@DrMathaholic sir but fx is entirely in terms of x and fy is entirely in terms of y so I could not solve simultaneously both the equations
@@TheBeast-gu9td okay..so in that case, u answer is correct...
All 4 points will come
@@DrMathaholic thanks sir
If delta1>0, delta2>0 and delta3
Then u cannot conclude. Test fails.
Thank you,sir!!
When delta 1 is 0 then which process we go through.. please upload sir
Then the test fails..
Sir, could you post the right answers please?
I have not solved the questions... 😀
Your answers are not matching with those in comment section?
1. Critical point (1,1) ,local minima
2. Critical point (-1/2,-1,3/2) , local minima
Thank you Om for posting the answer.