find the critical values of a multi-variable function and tell ưhether each are a global minimum, maximum, or saddle point in matlab in matlab

main.m
syms x y
f(x,y) = x^3 - 3*x + y^3 - 3*y;
gradf = gradient(f);
Hf = hessian(f);

critical_values = solve(gradf(1)==0,gradf(2)==0);
for i=1:length(critical_values.x)
    X = [critical_values.x(i);critical_values.y(i)];
    H = double(subs(Hf,{x,y},{X(1),X(2)}));
    
    if det(H)>0 && H(1,1)>0 %minimum
        disp(['(',num2str(X(1)),',',num2str(X(2)),') is a global minimum']);
    elseif det(H)>0 && H(1,1)<0 %maximum
        disp(['(',num2str(X(1)),',',num2str(X(2)),') is a global maximum']);
    elseif det(H)<0 %saddle point
        disp(['(',num2str(X(1)),',',num2str(X(2)),') is a saddle point']);
    else 
        disp(['Cannot tell the nature at (',num2str(X(1)),',',num2str(X(2)),')']);
    end
end

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