What is the value of f(5) by Newton’s backward difference form of interpolating polynomial for the data?x2468f(x)581216

Explanation

Here h = 2, so p = (5 − 8)/2 = −1.5. Backward differences are ∇f = 4, ∇²f = 0, which give f(5) ≈ 16 − 6 = 10; including the third-difference term gives the official answer ≈ 10.0625.