What is the value of f′(x) at x = 4 from the following table of values?

To estimate f'(x) at x = 4, we use the second-order backward difference formula since it is the last point in the table.

Formula: f'(x_n) ≈ [3f(x_n) - 4f(x_{n-1}) + f(x_{n-2})] / (2h)

Here, h = 1, x_n = 4, f(4) = 35, f(3) = 27, and f(2) = 22.

Substituting the values: [3(35) - 4(27) + 22] / 2 = [105 - 108 + 22] / 2 = 19 / 2 = 9.5.