Fixed the problem. In the second plot, my x(2) was in the wrong term. It should have been brought into the left parthensis. Here is the correct code:
xdata = [1;10;100];
ydata = [0;0;0.3];
fun = @(x,xdata)(1./(1+(x(1)./xdata).^x(2)));
lb = [170,1];
ub = [200,2];
x0 = [180,1.6];
%x = lsqcurvefit(fun,x0,xdata,ydata,lb,ub)
opts = optimset('MaxFunEvals',1E+4, 'MaxIter',1E+4 );
x = fminsearch(@(x) norm(ydata - fun(x,xdata)), x0, opts)
figure
hold on
plot(xdata,ydata,'ko');
xlim([0 200]);
xlabel('Concentration','FontWeight','bold');
ylim([0 1]);
ylabel('Average Mortality','FontWeight','bold');
box off
y = 0:600;
plot(1./(1+(x(1)./y).^x(2)))
xlim([0 200])
ylim([0 1])
