2.9 Embedding Octave

% Define a function handle
f = @(x) sin(x) .* exp(-x/5);

% Create a range of x values
x = linspace(0, 10, 100);

% Evaluate the function
y = f(x);

% Numerically approximate the derivative using diff
dx = x(2) - x(1);
dy = diff(y) / dx;
x_mid = x(1:end-1) + dx/2;

% Find a root near x = 3 using fzero
root = fzero(f, 3);
fprintf('A root of the function is approximately at x = %.4f\n', root);

A root of the function is approximately at x = 3.1416