Is there a smooth solution to minimize this: $\int_0^1{x \over {1+k^2f'(x)^2}}dx\\ f(0)=1\\ f(1)=0\\ f'(x)<=0\\ k^2>0\\\\$ I could "solve" it using a numeric approximation but would love to see an analytic solution (algebraic or not, doesn't matter). Thank you so much in advance. Fingers crossed.