What is the value of f(5) by Newton's backward difference form of interpolating polynomial for the data?

Explanation

Note: the answer key gives (C), but the cubic through these points gives f(5) = 16 + (−1.5)(4) + 0 − 0.0625 = 9.9375, which is not among the options. 10.0625 comes from taking the third-difference term with the wrong sign.