%question 1
clear all;
clc;

n = 5;          % Number of iterations
alfa = 0.5;     % Learning rate

% Define the function
syms x1 x2;
fx = 25*x1^2 + x2^2;

% Compute gradient
x = [1; 3];
c=zeros(1,2);

% Gradient descent iterations
for i = 1:n
    % Compute gradient at current point x
    c = double(subs(gradient(fx, [x1, x2]), [x1; x2], x))

    % Normalize gradient (optional step, for some methods)
    cbar = c / norm(c)

    % Update x using gradient descent formula
    x = x - alfa * cbar;

    % Evaluate the function at the new x
    fval = 25 * (x(1)^2) + (x(2)^2);

    % Display current iteration information
    disp(['Iteration ', num2str(i)]);
    disp(['x = ', num2str(x')]);
    disp(['f(x) = ', num2str(fval)]);
    disp('---');
end