function plotoptimal
u=0:.01:.99;
plot(u,fn(u));
hold on
plot([.84 .84],[0 fn(.84)])
U=.1;
u=[.47+.53*U 1-.53*U];
plot(u,fn(u),'ro')
u=[.47+.37*U .84-.37*U .84+.16*U 1-.16*U];
plot(u,fn(u),'g*')
u=[.47+.37*U   1-.16*U];
plot(u,fn(u),'b+')
xlabel('u')
ylabel('f(u)')