Hi Tatai,
When using MATLAB's spline function, it creates a piecewise polynomial (pp) form to represent the cubic spline. This form is used to interpolate the given data points. However, it seems there might be some confusion regarding the coefficients and the expected output.
Here's an example of how you might manually check or use a different method to see the cubic coefficients:
% Given data points
x = [3 4.5 6.5];
y = [12 17 38];
% Use the 'csape' function for a cubic spline with natural boundary conditions
cs = csape(x, y, 'variational');
% Display the coefficients
coefficients = cs.coefs
% Plot to visualize
xx = linspace(min(x), max(x), 100);
yy = ppval(cs, xx);
plot(x, y, 'o', xx, yy, '-');
title('Cubic Spline Interpolation');
xlabel('x');
ylabel('y');
