^{3}- x

^{2}+ 5, create the forward difference table. Range of values of x is -2 ≤ x ≤ 3

Ex 2. If y = x

^{3}+ x

^{2}- 2x + 1, calculate values of y for x = 0, 1, 2, 3, 4, 5 and form the difference table. Find the value of y at x = 6 by extending the table and verify that the same value is obtained by substitution.

Ex 3. Form the forward difference table for the function f(x) = x

^{3}+ 5x - 7 for x = -1, 0, 1, 2, 3, 4, 5. Continue the table to obtain f(6) and f(7).

Ex 4. Construct the table of differences for the data given below:

f(0) = 1.0, f(1) = 1.5, f(2) = 2.2, f(3) = 3.1, f(4) = 4.

Evaluate Δ

^{3}f(2).