clf
axis([-1 1 -1 1])
box on
hold on

h = 1/64;
x = -1:h:1;
w = x.*exp(x);
p(1) = plot(x,w);
p(2) = plot(w,x);

x = log(2)/2;
y = lambertw(x);
plot(x,y,'k.','markersize',18)

plot([-1 1],[0 0],'k')
plot([0 0],[-1 1],'k')
plot([-1 1],[-1 1],'k--')
set(p,'linewidth',1.5)

ebar = -1/exp(1);
text(-.8,.65,'z = -y/x','fontweight','bold')
set(gca,'xtick',[-1 ebar 0 x 1], ...
    'xticklabels',{'-1','-1/e','0','x = log(2)/2','1'})
set(gca,'ytick',[-1 ebar 0 y 1], ...
    'yticklabels',{'-1','-1/e','0','y','1'})
legend('x*exp(x)','lambertw(x)','location','northwest')
title('lambertw(x)')
hold