Hi, 1. The problem statement, all variables and given/known data A quadratic piecewise interpolation is carried out for the function f(x)=cos(πx) for evenly distributed nodes in [0,1] (h=xi+1-xi, xi=ih, i=0,1,...,πh). I am asked to bound the error. 2. Relevant equations 3. The attempt at a solution I believe the error in this case is bounded thus: |e(x)| ≤ [1/(n+1)!]max(f(n+1)(c))*max(∏[i=0,n](x-xi)) where c[itex]\in[/itex][0,1] hence, yielding [1/3!]*π3*2h3/(3√3) (1) First of all, is that correct? (2) Next, in case this is correct, why is it bounded thus instead of as in the case for f(x)=e-x in [0,1] where, generally, it is bounded thus: |e(x)| ≤ hn+1/(4*(n+1)) ?? I'd sincerely appreciate some insight, please.