In: Advanced Math
find Lagrange polynomials that approximate f(x)=x^3,
a) find the linear interpolation p1(x) using the nodes X0=-1 and X1=0
b) find the quadratic interpolation polynomial p2(x) using the nodes x0=-1,x1=0, x2=1
c) find the cubic interpolation polynomials p3(x) using the nodes x0=-1, x1=0 , x2=1 and x3=2.
d) find the linear interpolation polynomial p1(x) using the nodes x0=1 and x1=2
e) find the quadratic interpolation polynomial p2(x) using the nodes x0=0 ,x1=1 and x2=2