I recently started studying about global maxima and minima.
The extreme value theorem proves the existence of global maxima and minima for a continuous function in a closed interval.This theorem is actually, pretty much intuitive and looks like a basic property of a continuous function.
Has it got any applications other than just proving existence of global maxima or minima?
If you take a look at Lagrange's mean value theorem we can use it to prove inequalities like $|\cos(a)-\cos (b)|<|a-b|$.
So, I'm just looking for some cool stuff that you can do using the extreme value theorem.