You sir are awesome! I liked your deliberate and detailed way of explaining, "you understand". I had a question though about the last graph that is both a saddle point and a point of inflection, how were you able to tell from the graph that it was both? I thought you needed to work this out mathematically to prove that a saddle point does not exist just like you did with the cubic function.
Doublet point is more related with optics and lenses. You may explore those areas for better understanding. We do not use this term in 2D curve sketching. Thanks
To be a inflection point, along with concavity changes, we should have second derivative equal to zero. But in first graph at 22:50, how the points B and G became POI without we having any data about their second derivative ? Can we call any points changing concavity as POI ?? Sir, Could you please explain this ??
sir … 1. at point of inflection first derivative doesn’t change its sign where as second derivative changes its sign. 2. your explanation about saddle point and point of inflection is confusing because There are two kinds of points of inflection 1. stationary point of inflection where first derivative and second derivative both are zero 2. non stationary point of inflection where first derivative not equal to zero but second derivative zero or can be not defined … The example you gave x^3 + x has non stationary point of inflection at x = 0 … previously i saw one video of yours about random variable which i guess it is confusing as well
@@MathematicsTutor check IB books MATHS HL BY FABIO CIRRITO… even one of your video you are telling about random variable as …. they are not random and they are not variable … i feel you are not sharing correct knowledge which may misguide students…. this is my suggestion and rest upto you…
Now what is the difference between saddle point and point of inflexion? You also said the function is not differentiable at B why? . I think concavity changes at B which is clearly a point of inflexion
Please correct me if I am wrong. You said "point of inflection is independent of first derivative". How? I mean if first derivative is not zero then its not even a stationary point. I think it depends, for that first derivative must be zero at point of inflection.
I am from pakistan. Now i have clear my mind about saddle point interms of one variabe, b/s i have study saddle points related to two variables. If i am not wrong then i can say that y=x^2 has no saddle point.
Very informative video.......I'm also mathematics teacher but have doubts about it...... but now it is clear very well....
Great video with example explanations 💖💖💖✌️
Your teaching methodology is so good sir now i understood clearly
this really helped me I was failing to understand
Excellent explanation ,, thank you very much sir...
Very helpful sir ,great content 👏
A truly great video to help understand these 4 points.
Nice explanation sir❤
I am from IIT Kanpur. I like your graph approach to make me understand these topics.
Thanks a lot! You are from IIT Kanpur - The Best of the Best! I am honoured!
God bless you sir ❤❤❤❤
very well explained
super intro to this topic sir!!, really enjoyed it
Great!
Amazing 👏
clear and cute explanation
You sir are awesome! I liked your deliberate and detailed way of explaining, "you understand".
I had a question though about the last graph that is both a saddle point and a point of inflection, how were you able to tell from the graph that it was both? I thought you needed to work this out mathematically to prove that a saddle point does not exist just like you did with the cubic function.
Dear Sir, could you answer me, What difference between saddle and doublet point?
Doublet point is more related with optics and lenses. You may explore those areas for better understanding. We do not use this term in 2D curve sketching. Thanks
very well explained. I completely understand ..
Very good explanation
Excellent
At point B, F WHY IT IS UNDEFINED? explain
To be a inflection point, along with concavity changes, we should have second derivative equal to zero.
But in first graph at 22:50, how the points B and G became POI without we having any data about their second derivative ?
Can we call any points changing concavity as POI ??
Sir, Could you please explain this ??
Yes any point where concavity changes and where unique tangent exist is POI
Good explanation
Thanku🎉
sir …
1. at point of inflection first derivative doesn’t change its sign where as second derivative changes its sign.
2. your explanation about saddle point and point of inflection is confusing because
There are two kinds of points of inflection
1. stationary point of inflection where first derivative and second derivative both are zero
2. non stationary point of inflection where first derivative not equal to zero but second derivative zero or can be not defined …
The example you gave x^3 + x has non stationary point of inflection at x = 0 …
previously i saw one video of yours about random variable which i guess it is confusing as well
Point of Inflection is tested with Second derivative only
Thanks
@@MathematicsTutor
check IB books MATHS HL BY FABIO CIRRITO…
even one of your video you are telling about random variable as …. they are not random and they are not variable …
i feel you are not sharing correct knowledge which may misguide students….
this is my suggestion and rest upto you…
Now what is the difference between saddle point and point of inflexion? You also said the function is not differentiable at B why? . I think concavity changes at B which is clearly a point of inflexion
Point of inflection is surely the point where the concavity changes. Here second derivative is 0 or DNE
I have a doubt sir ,you said the critical point is when the f'(x) =0 or DNE , but slope of B is not 0 or DNE
Explain me sir
I'm confused 😢
We have vertical tangent at B. f'(B) DNE. Hope that helps. Thanks
@@MathematicsTutor means whenever we have a vertical tangent, f'(x) =DNE
Am i right sir ......🤐🤔
@@IITIAN_dost actualy tangent vertial means tanx, x=90, tanx= inf or undefined
Please correct me if I am wrong. You said "point of inflection is independent of first derivative". How? I mean if first derivative is not zero then its not even a stationary point. I think it depends, for that first derivative must be zero at point of inflection.
Point of inflection need not be a stationary point, but if it is, then it will also be a saddle point.
Thank you sir
this so good toffee but my calculus ma'am copy past from you then explain to me
I am from pakistan. Now i have clear my mind about saddle point interms of one variabe, b/s i have study saddle points related to two variables. If i am not wrong then i can say that y=x^2 has no saddle point.
Perfect
you just ripped maxima and minima