can you use direct search to find the intersection points for f(x) = sin5x and g(x)=0.1x and plot ti in matlab

main.m
% Define the functions
f = @(x) sin(5*x);
g = @(x) 0.1*x;

% Define the range of values for x
x = linspace(-2*pi, 2*pi, 1000); % Adjust the range as needed

% Evaluate the functions at each x value
f_values = f(x);
g_values = g(x);

% Find the indices where the functions have opposite signs
diff_sign_indices = find(diff(sign(f_values - g_values)));

% Initialize an array to store the intersection points
intersection_points = zeros(size(diff_sign_indices));

% Perform direct search to refine the approximation of the intersection points
for i = 1:length(diff_sign_indices)
    x1 = x(diff_sign_indices(i));
    x2 = x(diff_sign_indices(i) + 1);
    intersection_points(i) = fzero(@(x) f(x) - g(x), [x1, x2]);
end

% Plot the functions and intersection points
plot(x, f_values, 'b', x, g_values, 'r', intersection_points, f(intersection_points), 'ko');
legend('f(x) = sin(5x)', 'g(x) = 0.1x', 'Intersection points');
xlabel('x');
ylabel('y');
title('Intersection points of f(x) and g(x)');
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