Following the example given in class, construct a set of piece-wise quadratic polynomialsqj(x) (j=

0,1,2, ..., n1) to interpolate a set of n+1 points (xi, f(xi)), fori= 0,1, ..., nso that: (1)qj(xj) =f(xj) forj= 0,1,...,n1 andqj(xj+1) =f(xj+1) forj= 0,1,...,n1.

(2)qj(x) has continuous first order derivative at all the interior nodes.