某窗为半圆置于矩形之上，若此圆框的周长为一定值L，试确定半圆的半径r和矩形的高h，使所能通过的光线最为充足？
參考答案:L = 2h + (π + 1)r .........h = [L - (π + 1)r]/2
S = h*2r + (π*r^2 )/2
= [L - (π + 1)r]*r + π/2*r^2
= L*r - (π + 1)*r^2 + π/2*r^2
= L*r - (π/2 + 1)*r^2
S'= L - (π + 2)*r = 0
r = L/(π + 2)
h = L/[2(π + 2)] = r/2