how to find the range of x, y in a multivariable function in matlab

To find the range of a multivariable function in Matlab, you can use the fmincon function. fmincon is a built-in optimization function that can be used to minimize or maximize a function subject to constraints.

To find the range of a function over a certain range of x and y, you can define a function handle that takes in x and y as inputs and outputs the value of the function. You can then use fmincon to minimize or maximize this function over the range of x and y.

Here's an example:

main.m
% Define the multivariable function
fun = @(x,y) x.^2 + sin(y);

% Define the range of x and y
x_range = [-1, 1];
y_range = [-pi/2, pi/2];

% Set up the constraints for fmincon
A = [];
b = [];
Aeq = [];
beq = [];
lb = [x_range(1), y_range(1)];
ub = [x_range(2), y_range(2)];

% Use fmincon to minimize or maximize the function
min_val = fmincon(fun, [0, 0], A, b, Aeq, beq, lb, ub);
max_val = fmincon(@(x,y) -fun(x,y), [0, 0], A, b, Aeq, beq, lb, ub);

% Display the range of the function
fprintf('Range of function over [%d,%d] x [%d,%d]: [%f,%f]\n', x_range(1), x_range(2), y_range(1), y_range(2), min_val, max_val)
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In this example, we've defined a multivariable function fun(x, y) = x^2 + sin(y), and we're finding the range of the function over the range [-1, 1] x [-pi/2, pi/2]. We set up the constraints for fmincon to restrict the values of x and y to be within the range, and then use fmincon to minimize and maximize the function over this range. Finally, we display the range of the function.