using 'fsolve'

I have the function f(x,y) = x.^(2-x.^(0.5))+y.^(2-y.^(0.5)) and I found the Jacobian and Hessian Matrices. Now I need to find the turning point using the function "fsolve" and stating its nature.

Can anyone help me?

Thanks in advance.

[Walter Roberson]

The "turning points" are all the points where the derivative are 0.

You already have the derivative when you formed the Jocobian.

Answer 1

[Stephan]

Hi,

why not solve it symbolic:

syms f(x,y)
f(x,y) =  x.^(2-x.^(0.5))+y.^(2-y.^(0.5));
[xsol,ysol] = vpasolve(diff(f,x) + diff(f,y) == 0, [x,y], [1 3; 1 3]);
zsol = subs(f,[x,y],[xsol,ysol]);
% plot results
fsurf(f)
hold on
scatter3(double(xsol),double(ysol),double(zsol),'or','LineWidth',2,'MarkerFaceColor','r')