Session 9: Hessian matrix to find Local maxima, Local minima, Saddle point of a function.

[@607]

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.

[@DrMathaholic]

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..👏👏

[@abhaykhade539]

Heartly congratulations sir ji...🎊🎉 1k subscribe milestone complete before 1 day of ESE

[@DrMathaholic]

Thank you Abhay😊

[@OpQp-mc3tr]

amazing content sir please keep helping us and also come back to coep

[@DrMathaholic]

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

[@OpQp-mc3tr]

@@DrMathaholic 🥺

[@mohsinali-10]

Phenomenal explanation. Thank you!

[@DrMathaholic]

Thank you 😊

[@ghezaegoitom4429]

Thank you so much, I enjoyed every minute of your lecture

[@DrMathaholic]

Welcome and happy to hear that 😊

[@thenewdimension9832]

Thankyou so much sir ❤❤❤

[@madhavigole178]

1) Critical point (-3,3) - local minima 2) Critical point (-1/2,-1,3/2) - local minima

[@DrMathaholic]

Thank you Madhavi for posting the answer.. appreciated!!

[@madhavigole178]

Sir, is saddle point same as point of inflection?

[@makeitsimple2306]

Thank you from iraq

[@DrMathaholic]

Thank you for your wishes and welcome 😊

[@mohammadrezazebardast3995]

Wish the bests for you

[@DrMathaholic]

Thank you 😊

[@AJ-et3vf]

Awesome video! Thank you!

[@DrMathaholic]

Welcome:)

[@siddharthm16]

Explained Well. Thanks.

[@DrMathaholic]

Glad to hear that.. thank you :)

[@malharpujari1144]

Thank you so much sir ☺️

[@DrMathaholic]

Welcome:)

[@kamrulhassan7157]

Thank you sir ❤

[@DrMathaholic]

@@kamrulhassan7157 welcome 😊

[@abedulkareemqasim9441]

YOU ARE GENIOUS

[@DrMathaholic]

@abedulkareemqasim9441 thank you for your kind words 😊

[@shreeniketfatangare668]

Thank you so much Sir!! All the videos were very helpful ! When will we be seeing the video on Langrange's multipliers?

[@DrMathaholic]

Welcome. Glad to hear that..

[@DrMathaholic]

About Lagrange multipliers,its late now.. Nobody asked me before and now I am on Diwali vacation till 17th.

[@hesammoradi8962]

dude you saved me

[@DrMathaholic]

Welcome 😀

[@vishnupantpotdar7610]

Really nice sir ji

[@DrMathaholic]

Thank you Vishnu.😀 Hope you r doing well 😀

[@user-iv2yc9yt7j]

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

[@DrMathaholic]

Thank you.. Oh okay.. Thanks for pointing it out..

[@NasrinSultana-jx4lm]

Thank you sir.

[@DrMathaholic]

Welcome 🙂🙂

[@nagmaniprasad203]

Sir, kindly make an video on quadratic forms

[@DrMathaholic]

Sure.. I will try soon..

[@abhirajrathod5677]

Sir, please can you upload a video on Langrange's multipliers?

[@DrMathaholic]

Its bit late to ask dude. I am at my home for Diwali.. So next video, may be after 18th..

[@ailebao9176]

Sir, if delta1 is zero, what we get? Can you explain for me? Thank you.

[@DrMathaholic]

Then the test fails we cannot conclude..

[@CHRISKASSMUKEN]

Thank you.

[@DrMathaholic]

Welcome 😀

[@cocomatef]

where you got the x^4 from??

[@DrMathaholic]

At what timestamp ??

[@francoisguyvignon]

I was looking for a proof for this - maybe just the 2D case for starters. Anyone has a reference?

[@DrMathaholic]

See book by Thomas calculus

[@TheBeast-gu9td]

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)?

[@DrMathaholic]

For safer side, check whether these 4 (x,y) points satisfy fx and fy or not..

[@TheBeast-gu9td]

@@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

[@DrMathaholic]

@@TheBeast-gu9td okay..so in that case, u answer is correct... All 4 points will come

[@TheBeast-gu9td]

@@DrMathaholic thanks sir

[@prabalsarkar3210]

When delta 1 is 0 then which process we go through.. please upload sir

[@DrMathaholic]

Then the test fails..

[@simranmanghwani3514]

If delta1>0, delta2>0 and delta3

[@DrMathaholic]

Then u cannot conclude. Test fails.

[@simranmanghwani3514]

Thank you,sir!!

[@komalkamaram733]

Sir, could you post the right answers please?

[@DrMathaholic]

I have not solved the questions... 😀 Your answers are not matching with those in comment section?

[@omgawande1567]

1. Critical point (1,1) ,local minima 2. Critical point (-1/2,-1,3/2) , local minima

[@DrMathaholic]

Thank you Om for posting the answer.