f(x)=cos(49x2)−sin(14x) has a local minimum, the smallest in absolute value is: in matlab

To find the local minimum of the given function, we can use the fminsearch function in MATLAB, which is an optimization function that tries to find the minimum of a given function. Here is how we can use it for the given function:

main.m
% Define the function
f = @(x) cos(49*x^2) - sin(14*x);

% Use fminsearch to find the minimum
x0 = 0; % Starting point for optimization
[x_min, f_min] = fminsearch(f, x0);

% Display the result
fprintf('The smallest local minimum of f(x) = cos(49x^2) - sin(14x) is:\n');
fprintf('x = %f\n', x_min);
fprintf('f(x) = %f\n', f_min);
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After running this code, the result will be printed to the console, showing the value of x at which the minimum occurs, as well as the value of the function at that minimum.