Understanding Concave and Convex Functions

[@viktorszasz6771]

My man! This is the best explaination I've found, yet I've searched in 3 languages. Great explaining, awesome visualisation, simply an incredible video and a great help! Thank you very much!!!!

[@vaishakmuralidharan7605]

Been breaking my head over understanding jensen's inequality, this was a really clear, unassuming explanation! Thank you a ton

[@chandradeepraut9306]

Same with me watched it for trigono

[@shireenkhan6847]

hey, any other resources you can tell which can help with Jensen's inequality too? I can't understand it at all

[@sharonlima8913]

what do you mean by unassuming function?

[@JhoiverJimenez]

@@shireenkhan6847 what about this one? kzbin.info/www/bejne/goDam2qLrbaqgJI

[@JhoiverJimenez]

@@sharonlima8913 function? Perhaps you meant explanation. In my case I feel the same, other math professors always assume we remember some concepts and aspect, some of us dont and when they assume we get easily lost in the subject.

[@dindor138]

Now the defination do not seem daunting at all after you've explained the design of the defination. Very helpful to me. Thank you.

[@awesomebearaudiobooks]

6:37 that is the face of my Brain when trying to understand Concave and Convex Functions.

[@brookecribbs4018]

bro why I am watching this for my econ class when I took Calc 1, 2, and 3 years ago and I just so lost

[@debasishguha6835]

Explained a pretty complicated topic very nicely. It is easy to visualize and understand the definition after watching this video. However, the points x and y are chosen such that f(L) > both f(x) and f(y). I have been trying to convince myself how this would have worked if y was such that f(y) was more around the crest and f(L) in that case would have lied between f(x) and f(y).

[@omniscienceisdead8837]

im coming in from time series for deep learning , keep it up broo

[@huntergiles]

I have been stuck on this for days. thank you so much

[@mightym3209]

Simply best! Thank you for such a detailed and step-by-step explanation.

[@RayRay-yt5pe]

Thank you very much. You've just gained a new subscriber.

[@abdoennajah2702]

Finally i understood. Thank you for this great explanation

[@N0N5T0P]

Excellent video!!! The only thing I'm wondering about is about the strictly convex/concave functions. It seems to me that whenever lambda is either 0 or 1, the two sides of the "inequality" will always be equal. You even mentioned that in your video. But how can we EVER have a strictly convex/concave function then, with this definition? Do you have to change lambda to be 0

[@jasminewong2010]

Thanks ! This is so helpful and breaks it down really easily

[@clementecarbonaro619]

thank you so much, you explained it exceptionally well

[@victoriacorcimaru1731]

Honestly, a brilliant explanation! 🤩 Short question: other videos on this topic talk about taking the weighted average of x and y. How/where does that fit within your explanation, sir?

[@slavojivaneie1924]

Tl;dr the "weighted average" stuff is supposed to motivate Jensen's inequality from probability. Read "f(E[X])" as "a function of weights" and "E[f(X)]" as "the weighted average of functions." If we apply the probability weights (t,1-t) to the interval endpoints a and b, we get ta+(1-t)b = W1, and if we apply the same weights to corresponding maps of the endpoints, f(a) and f(b), we get tf(a)+(1-t)f(b) = W2. The function f is concave over [a,b] if, for all weights (t,1-t), f(W1) ≥ W2. In other words, the value of a function of the weights (LHS) vs. the value of a weighted function (RHS). Jensen's inequality states that if f is *convex* (so f(W1) ≤ W2), and X is a random variable, then f(E[X]) ≤ E[f(X)]. If we think of taking the expectation of X as applying weights to the values that X can take on, then obtaining the expected value E[X] is much like getting W1. Thus, f(E[X]) is analogous to f(W1). Likewise, if we think of E[f(X)] as the weighted average of the random variable Y=f(X), then E[f(X)] weights f(X) to obtain W2.

[@victoriacorcimaru1731]

@@slavojivaneie1924Wow! Thank you!

[@FatjonZepol]

I really appreciate your efforts! Could you help me with something unrelated: I have a SafePal wallet with USDT, and I have the seed phrase. (alarm fetch churn bridge exercise tape speak race clerk couch crater letter). What's the best way to send them to Binance?

[@gunterjohann4417]

that is a truly great video.

[@SaranshGupta786]

Very clear explanation, thanks a lot.

[@SterlingRamroach]

If you pick an x or y such that f(x) or f(y) is the max value on the y-axis, then based on lambda, the right side of the eqn can be either < or > f(L). For example if the "curve" is a straight line. Also, if LHS == RHS, how can you tell if it's convex or concave?

[@amberxv4777]

Good question. I'd be willing to say that if f(x) or f(y) value were to endat infinity, then it would be neither concave or convex function. But we need confirmation

[@helawlodar9070]

thank you! this was very helpful!!!

[@nocontextnikhil]

amazing explanation

[@zainabhaider4369]

maybe a question. Why do we derive twice! We do not equate the first derivative with zero, as in Rolle's theorem.!! Why do we derive twice and not 3 or 4 times?

[@josephm276]

Excellent sir🌹🌹🌹🌹

[@hritikawadhawan6707]

Can you post a video on how to do sums of this type

[@imaadnaeemansari8693]

Great explanation!!

[@rohan45]

Great explanation Thank you so much

[@PriyanshuJain-c8v]

Insanely good, thanks a ton

[@bilenkeziban6237]

Well explained, thank you!

[@jakobnilsson4704]

Awesome explanation

[@nq2c]

this was super helpful thank you!

[@orlandoheredia2380]

Hey, good explanation, but about the strictly concave function, the λ should be ]0,1[, right ? Because if lambda can be 0 or 1, there would be a paradox as f(x) > f(x) in that case.

[@jayneabrown]

Super helpful. Thank you so much.

[@swatisingh559]

This is really good⚘️⚘️

[@ouafaeraibi7847]

amazingly explained, Thank you!

[@mohammedchowdhury4218]

could you please help me understand how to check if this function f(x,y)=xy. How is it concave and how do I do the check for it

[@sigmamathematics2215]

I got understand 1st time ❤❤❤

[@zainislam554]

can you please confirm that how to find f(x) and f(y) , the points placed on vertical axis?

[@dirkadrichem5468]

How about the sine and cosine function?

[@deeptysarder6797]

Nice graphical explanation

[@law9544]

What are u guys majoring in?

[@primeview921]

I have a problem understanding the nature of f. Is it a function a single variable or more?

[@rodrigocalixto470]

I don't get it, how can you compare a point, f(λx+(1-λ)y), with a line f(λx) + (1-λ)f(y)?

[@arwaalshikrian5354]

Extremely helpful

[@pratiksahu173]

I got this... 😊 Thanks a ton.. !!

[@devinahluwalia9289]

Was very helpful, cheers 🍺

[@sreyanjali]

this was very helpful

[@viniciusbrilhante5112]

That was a really good explanation! Very clear!

[@shubrajchuckowree5670]

excellent, but better use x1 and x2 rather than x and y to avoid confusion

[@rishiraj5711]

Thanks for this.❤

[@hypebeastuchiha9229]

That was really helpful thanks

[@muzaffert]

Appreciated🙏

[@dikshabagh30]

really good video

[@NNKNTA]

Bro, sorry for my cheap english, but God will bless you :*

[@mrak8948]

Grt explanation

[@voyagers5026]

just great thanks a lot

[@iulianatoropoc5016]

Eureka! She cried.

[@solounomas0]

And why is this for?

[@haqseiitian]

thankyou bro...

[@swatisingh3327]

❤❤❤❤wow

[@albmrbo1]

Thank you!

[@fragamus]

Exetra->et cetera

[@williamgamelin154]

Well dons and thanks for memory boost.

[@j.brightlee3314]

plz do more video plz plz

[@denvernarvasa3033]

thank you :)

[@handleyt2024]

legend

[@JessaEstrada1315]

thanks!

[@xhonimehmeti9432]

wasted 22 min of my life

[@indian_otaku2388]

wasted 10 seconds of my life

[@AMANDHOL-f7v]

The content is okay, but brother you have to work on your speech , you're very monotonours.