By the way, with respect to your recent question that you deleted:
[X,Y]=meshgrid(x,y);
X and Y will both be 2D arrays.
f=2.25*X.*Y+1.75*Y-1.5*X.^2-2*Y.^2;
f is built from 2D arrays, so f will be a 2D array.
fun = @(z)-2.25*X.*Y-1.75*Y+1.5*X.^2+2*Y.^2;
You accept an input but ignore it and always return the same thing that was calculated and stored into f.
You could change the @(z) to @(f) but that would not make any difference.
z = fminsearch(fun,x0)
the function you pass to fminsearch must return a scalar, not an array.
I suspect what you want is
fun = @(XY)-2.25*XY(1).*XY(2)-1.75*XY(2)+1.5*XY(1).^2+2*XY(2).^2;
Note, by the way, that you can calculate the optimum using calculus instead of fminsearch. When f is of the form
A*X.*Y + B*Y - C*X.^2 - D*Y.^2
then
x = -(A*B)/(A^2 - 4*C*D)
y = -(2*B*C)/(A^2 - 4*C*D)
is the critical location. (Caution: you really should check whether it is a minima or maxima)
