(30pt) Construct the Newton form of the interpolating polynomial p(x) of degree
2 that satisfies the following:
p(0)=1,p(1)=3, and p^(')(1)=2.
You may want to use the divided difference table and the following recur-
sive relation that for x_(n)!=x_(0),
f[x_(0),x_(1),cdots,x_(n)]=(f[x_(1),cdots,x_(n)]-f[x_(0),cdots,x_(n-1)])/(x_(n)-x_(0)).
2. (30pt) Construct the Newton form of the interpolating polynomial p(x) of degree 2 that satisfies the following:
p(0)=1,p(1)=3,and p(1)=2.
You may want to use the divided difference table and the following recur- sive relation that for xn xo,
Tn-To