Chapter 10.3, Problem 2QQ

Find the interpolating polynomial of the following point and function using Newton's interpolation process. y = ln ( x + 2 ) at x = [-1,2]. Find the interpolating polynomial of the following function using Direct Fit Polynomials. y = exp( 2-x ) at x = [-1,2].

Prove that if the (n + 1) th derivative of a polynomial vanishes but the nth does not, then the polynomial has degree n.

A function fl x) passes through the points (15,24), (18,37), and (22.25). Use Newton's Divided Difference Method to interpolate a quadratic polynomial approximation of f(x) Use this to approximate the value of the first derivative f(17). -2.9999 O none of the choices O -0.0047 O 3.2857