# Thread: Need help with a problem on Optimisation

1. ## Need help with a problem on Optimisation

Please help me with finding the function u, which gives the minimal value of the integral from 0 to 1:

Int(u'(x)^2+u(x))dx--> min

with conditions:

Int(u^2(x))dx=1 (integral is from 0 to 1)
u'(0)=u'(1)=0

Where u has a continuous derivative.

2. Well i know e^x has a continuous derivative, so consider than function, just giving some input, maybe wrong.

3. Originally Posted by RockHard
Well i know e^x has a continuous derivative, so consider than function, just giving some input, maybe wrong.
it is not so simple problem)

4. That is a "calculus of variations" problem. Calculus of variations - Wikipedia, the free encyclopedia

Do you know the corresponding "Euler-Lagrange" equation?