Construct a forward difference table for y = f(x) = x³+2x+1 for x = 1,2,3,4,5

Prove that f(4) = f(3) + Δf(2) + Δ² f(1) + Δ³ f(1) taking ‘1’ as the interval of differencing.

Given y₃ = 2, y₄ = −6, y₅ = 8, y₆ = 9 and y₇ = 17 Calculate Δ⁴y₃

Evaluate ∆(log ax).

If f(x) = x² + 3x then show that Δf(x) = 2x + 4