among the locations at which the function f(x)=cos(12164x2)−sin(114x) has a local minimum, the smallest in absolute value is: in matlab

You can use the fminbnd function in MATLAB to find the local minimum of a function. Here's an example of how to use it on the given function:

main.m
% Define the function
f = @(x) cos(12164*x^2) - sin(114*x);

% Use fminbnd to find the local minimum
[xmin, fmin] = fminbnd(f, 0, 1);

% Display the result
fprintf("The smallest local minimum is f(%f) = %f.\n", xmin, fmin);
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This code sets up an anonymous function f that represents the given function, then uses fminbnd to search for the local minimum between 0 and 1. The function returns the location of the minimum (xmin) and the function value at that location (fmin). The code then prints out the result.

Note that this code assumes that the smallest local minimum is somewhere between 0 and 1. If the smallest local minimum is outside this range, you'll need to adjust the inputs to fminbnd accordingly.