How to calculate the maximum distance between two functions

Hello guys i have a test on matlab coming up in the university , one of the exercises is probably going to be to calculate the maxium distance between two functions.

ex.

f1=cos(x) f2=sin(x) x=[0,4pi]

find the x for which the distance between f1 and f2 is maximum

Answer 1

[Torsten]

x = fminbnd(@(x)-(sin(x)-cos(x))^2,0,4*pi)
distance = abs(sin(x)-cos(x))