Well i know e^x has a continuous derivative, so consider than function, just giving some input, maybe wrong.
Please help me with finding the function u, which gives the minimal value of the integral from 0 to 1:
Int(u^2(x))dx=1 (integral is from 0 to 1)
Where u has a continuous derivative.
That is a "calculus of variations" problem. Calculus of variations - Wikipedia, the free encyclopedia
Do you know the corresponding "Euler-Lagrange" equation?