How to prove continuity, single-valuedness and continuos slope of a function in MATLAB?

Hi, I would like to test a function's acceptable character to the Schrödinger eqn, and have the three following criteria to check:

1. That the function f(x) is single-valued everywhere 2. That the function f(x) is continuous. 3. That the derivative of f(x) is continuous everywhere.

How can I find this out in MATLAB on the example case f(x) = e^ix*cos(x) ?

Thanks!

[Adam]

Surely those are analytical questions since you have an analytical function. Matlab works with discrete data so trying to use it to prove something is continuous doesn't seem worthwhile.

[Sergio Manzetti]

That is rather disappointing, as those criteria are the fundamental prescriptions to QM.