3. From a function, f(x), we obtain the following data points: ($x_i$, f($x_i$)) = {(-0.5, e), (0, 1), (0.5, $e^{-1}$)}.
(a) (5 marks) Using the Newton/Divided-Difference method, find the interpolating polynomial for f(x) using
the data points above, and using it evaluate the approximate value of f(0.25).
(b) (3+2 marks) State Cauchy's Theorem (Do not need to prove). Now suppose a function f(x) is five times
differentiable, and it is interpolated by a degree five polynomial. Explain or state what would be the interpolation error.