estimate f’(x) at xi =𝟏, using both forward and centered finite difference in matlab

To estimate f’(x) at xi=1 using both forward and centered finite differences in MATLAB, you can use the following code:

main.m
% Define the function f(x)
f = @(x) x^2 - 5*x + 6;

% Define the value of xi at which you want to estimate the derivative
xi = 1;

% Define the step size
h = 0.01;

% Forward difference approximation
f_prime_forward = (f(xi + h) - f(xi)) / h;

% Centered difference approximation
f_prime_centered = (f(xi + h) - f(xi - h)) / (2*h);

% Display the results
disp(['Forward Difference Approximation: ', num2str(f_prime_forward)]);
disp(['Centered Difference Approximation: ', num2str(f_prime_centered)]);
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In this code, we define the function f(x) using an anonymous function. Then, we specify the point at which we want to estimate f’(x) (xi = 1) and the step size (h = 0.01).

Using the forward difference approximation, we calculate the derivative by subtracting f(xi) from f(xi + h) and dividing the result by h.

For the centered difference approximation, we calculate the derivative by subtracting f(xi - h) from f(xi + h) and dividing the result by 2h.

Finally, we display the results using the disp() function.

Please note that this code assumes a scalar function f(x). If you have a vector-valued function, you will need to modify the code accordingly.