Estimating the derivative by differentiating the interpolating cubic polynomial

Good afternoon guys,

I'm having a bit of trouble understanding how I would go about estimating the derivative of a function using this technique.

I'm given some function values (x), and I know I am required to use this function:

 p = spline(x,fx);

[Matt J]

I know I am required to use this function

How do you know that?

[Yakub Shalmiyev]

Because my professor has suggested this.

Answer 1

[Bruno Luong]

% Dummy test data
x=cumsum(rand(1,7));
y=rand(size(x));

ppf=spline(x,y);

% Derivative
ppdf = ppf;
ppdf.order=ppdf.order-1;
ppdf.coefs=ppdf.coefs(:,1:end-1).*(ppdf.order:-1:1);

% Check
close all
xi=linspace(min(x),max(x));
yi=ppval(ppf,xi);
plot(x,y,'o',xi,yi,'b');
xlabel('x');
ylabel('f(x)');
yyaxis right
dyidx=ppval(ppdf,xi);
plot(xi,dyidx,'r');
ylabel('df/dx(x)');
grid on