Given f(x,y), how do I solve gradient f=0?

I have a function f(x,y) and want to find the values of x and y that make grad(f)=0. Is is possible to do the gradient symbolically inside an m file? I'm trying to use 'gradient' and 'fsolve' commands, but getting hung up on syntax.

The function is: f=-(x.^2+(y-1).^2+x).*exp( -(x.^2+y.^2)/5 )

Answer 1

[Star Strider]

Two options — choose the one that works for you:

% % ————— Numeric:
x = linspace(-10, 10);
[X,Y] = meshgrid(x);

f = @(x,y) -(x.^2+(y-1).^2+x).*exp( -(x.^2+y.^2)/5 );

fxy = f(X,Y);
dxy = x(2)-x(1);
gfxy = gradient(fxy, dxy, dxy);

figure(1)
C = contour(X, Y, gfxy, [0; 0]);
grid on

% % ————— Symbolic: 
syms x y 

f = symfun(-(x.^2+(y-1).^2+x).*exp( -(x.^2+y.^2)/5 ), [x, y]);

gradfxy = gradient(f, [x, y]);

grad_zero = solve(gradfxy == 0);
x_soln = grad_zero.x
y_soln = grad_zero.y

Answer 2

[achraf Elqarnani]

x = linspace(-10, 10);

[X,Y] = meshgrid(x);

f = @(x,y) -(x.^2+(y-1).^2+x).*exp( -(x.^2+y.^2)/5 );

fxy = f(X,Y);

dxy = x(2)-x(1);

gfxy = gradient(fxy, dxy, dxy);

figure(1)

C = contour(X, Y, gfxy, [0; 0]);

grid on

% % ————— Symbolic:

syms x y

f = symfun(-(x.^2+(y-1).^2+x).*exp( -(x.^2+y.^2)/5 ), [x, y]);

gradfxy = gradient(f, [x, y]);

grad_zero = solve(gradfxy == 0);

x_soln = grad_zero.x

y_soln = grad_zero.y