suppose f(x) = exp(x), and we want to find f’(x) at xi =𝟏. estimate f’(x) at xi =𝟏, using both forward and centered finite difference in matlab

To estimate the derivative of f(x) = exp(x) at xi = 1 using forward and centered finite difference methods in MATLAB, you can follow these steps:

1. Define the function f(x) = exp(x):

main.m
f = @(x) exp(x);
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2. Choose a small value for step size h (e.g., h = 0.001) which determines the accuracy of the approximation.

3. Calculate the forward difference approximation of f'(x) at xi = 1 using the formula:

main.m
xi = 1;
h = 0.001;
forward_diff = (f(xi + h) - f(xi)) / h;
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4. Calculate the centered difference approximation of f'(x) at xi = 1 using the formula:

main.m
centered_diff = (f(xi + h) - f(xi - h)) / (2 * h);
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5. Finally, display the results:

main.m
disp("Forward Difference Approximation: " + forward_diff);
disp("Centered Difference Approximation: " + centered_diff);
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Here's the complete code snippet:

main.m
f = @(x) exp(x);
xi = 1;
h = 0.001;

forward_diff = (f(xi + h) - f(xi)) / h;
centered_diff = (f(xi + h) - f(xi - h)) / (2 * h);

disp("Forward Difference Approximation: " + forward_diff);
disp("Centered Difference Approximation: " + centered_diff);
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When you run this code snippet, you will get the forward and centered difference approximations of f'(x) at xi = 1.