Prove that every continuous piecewise affine function based on the mesh points x0

where

(a) What are the values of a and b?
(b) Write the hat function (11.168) in the form (11.179) .
(c) Write the piecewise affine interpolant constructed in Exercise 11.6.12(c), in the form (11.179) .
Remark: The multidimensional version of (11.179) , in which the absolute value is replaced by the Euclidean norm ||x||, is the simplest of a powerful new class of multivariate interpolation schemes known as radial basis functions, [9].

f(x)=ax + b + c, lx-xil, (11.179) f(a f(x (x)-f(x) 2 (xx) 2 (x-)