Understanding Concave and Convex Functions

In this video I break down the formal definition of a concave function and attempt to explain all aspects and variables used in the definition. Being that a convex function is just the opposite in terms of its definition, once one of them is well understood the other is also understood.

If anyone has any questions or is still unsure on any concepts covered in the vid put them in the comment section and il try my best to answer.

[viktorszasz]

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!!!!

[vaishakmuralidharan]

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

[dindor]

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

[debasishguha]

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).

[mightym]

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

[huntergiles]

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

[abdoennajah]

Finally i understood. Thank you for this great explanation

[awesomebearaudiobooks]

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

[NNTP]

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<lambda<1 instead of 0=<lambda=<1 perhaps (when trying to show strict convexity/concavity)?

[RayRay-ytpe]

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

[omniscienceisdead]

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

[SaranshGupta]

Very clear explanation, thanks a lot.

[rodrigocalixto]

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)?

[victoriacorcimaru]

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?

[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?

[zainabhaider]

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?

[orlandoheredia]

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.

[mohammedchowdhury]

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

[zainislam]

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

[primeview]

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