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.