Just as the problem says, use conditions (i) and (ii).

With , " " becomes and " " becomesand. " " becomes . Saying that " means the derivative must be continuous at : .

There are a number of additional conditions you could add- you could require a specific derivative at either endpoint. Another condition is the "not a knot" condition- requiring that thesecondderivative be continuous at as well- which would be equivalent to having a single quadratic function through the three points.