MATLAB: Finding the null gradient

fsolvegradient

Hello, I'm kind of struggling with a problem.

syms x y
g = gradient ([x^2 + x, y^2 - y], [x, y])

How can I determine [x, y] which make the gradient vector null?

I tried to use fsolve but couldn't get it to work.

A bit lost here. tks

See if this does what you want:

syms x y
f = [x^2 + x, y^2 - y];
g1 = gradient(f(1), [x, y]);
g2 = gradient(f(2), [x, y]);
x0 = solve(g1 == 0)
y0 = solve(g2 == 0)

It is because your function f is not updated. Here is what you need to do.

syms x y z
 f = x^2 + x + y^2 - y;
 f = subs(f,y,z);
 g = gradient(f, [x,z])

The result is

 g =
 2*x + 1
 2*z - 1

f=@(x,y) [x+y^2-5; x+y-3];
z = fsolve(@(p) f(p(1),p(2)),x0);