Given a vector x and corresponding function values y, which MATLAB code correctly computes the numerical derivative using central difference for interior points?

hard📝 Application Q9 of 15

MATLAB - Numerical Methods

Ady = diff(y) ./ diff(x);

Bdy = (y(2:end) - y(1:end-1)) ./ (x(2:end) - x(1:end-1));

Cdy = (y(3:end) + y(1:end-2)) ./ (x(3:end) - x(1:end-2));

Ddy = (y(3:end) - y(1:end-2)) ./ (x(3:end) - x(1:end-2));

Step-by-Step Solution

Solution:

Step 1: Recall central difference formula for vectors
Central difference at point i uses (y(i+1) - y(i-1)) / (x(i+1) - x(i-1)).
Step 2: Match code to formula
dy = (y(3:end) - y(1:end-2)) ./ (x(3:end) - x(1:end-2)); computes this for interior points correctly using vector indexing.
Final Answer:
dy = (y(3:end) - y(1:end-2)) ./ (x(3:end) - x(1:end-2)); -> Option D
Quick Check:
Central difference vector formula = dy = (y(3:end) - y(1:end-2)) ./ (x(3:end) - x(1:end-2)); [OK]

Quick Trick: Central difference uses neighbors two steps apart [OK]

Common Mistakes:

Using forward difference formula for central difference
Adding y values instead of subtracting
Ignoring vector indexing limits

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Given a vector x and corresponding function values y, which MATLAB code correctly computes the numerical derivative using central difference for interior points?

Step 1: Recall central difference formula for vectors

Step 2: Match code to formula

Final Answer:

Quick Check:

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