% Newton's Polynomial solver

X=sort(rand([10,1])*2*pi);

Y=sin(X);

%(X,Y) are the points to interpolate.

x=linspace(0,2*pi,200);

a=polyNewton(X,Y);

y=arrayfun(@(x) interpNewton(a,X,x), x);

function a=polyNewton(X,Y)

a=zeros(size(Y));

end

function y=interpNewton(a,X,x)

end

Question 1. For this test, you need to write two functions: polyNewton (X,Y) and interpNewton (a,X,X). X and Y are vectors which contains the values to be interpolated. polyNewton (X, Y ) returns a vector with the coefficients of the Newton's polynomial. interpNewton (a,X,x) uses the output of polyNewton and X to calculate the interpolated values at points contained in x. The twist is that you are allowed one and only ONE for-loop in each function AND you are not allowed to allocate any extra memory aside from a, which stores the output in polyNewton, and y which stores the output in interpNewton (the dummy