% Floating sphere problem
% x = depth at which sphere floats
% x will satisfy 0 <= x <= 2
% radius is 1 unit
% rho is specific gravity of sphere

% Try rho = 0.25 (cork ball)

% Note how we define a function of one variable
% to use in fzero
f = @(x,rho) x^3  -3*x^2 + 4*rho
opt = optimset('display', 'iter');
height = fzero( @(x) f(x,0.25), 1, opt)