# Help maximizing this functional please (it's simple, i think)

1. Jan 24, 2012

### enfield

the functional is $$\int_0^b{\frac{f(b)-f(x)}{b-x}},$$. Another thing is it has defined endpoints. $$f(0)=0$$ and $$f(b) \in (0,10)$$ and also $$f'(x)>0.$$ oh and $$b \in (0,\infty)$$

The euler-lagrange equation didn't give me anything helpful (not sure why..). One thing that is clear when looking at the functional is that very concave functions seem to maximize it, and very convex functions seem to minimize it.

so maybe the maxima/minima are (in the limit) the two halves of the rectangle defined by $$(0,0), (b,0), (b, f(b)), (0, f(b))$$. maybe.