How to know whether a function is convex or non convex

#1

In many algo. sir told that this function is convex or non convex,how just by looking at it we can say whether this is convex or not.
I know what sir in beginning sir told about the convex functions but how to identify them…???

#2

Just by looking at a random function we can’t say whether it is a convex function or not.

A way to check if a function is convex is by checking if it has a positive semidefinite hessian matrix everywhere.

You can check out this paper if you want a mathematical background about convex functions - http://www.math.cmu.edu/~ploh/docs/math/mop2013/convexity-soln.pdf