Do not apply any rou The population, f, of a small community on the outskirts of a city grew rapidly over a six year period, as can be seen in the table: X f(x) 0 ounding. 52 Using the 2 97 4 194 6 318 Here X denotes time (in years), while f(x) represents the size of the population of the community at time x. In what follows, apply the indicated numerical differentiation formula, obtained from Taylor's Theorem, with: h=2 Using the a) two-point forward difference formula, the instantaneous rate of change of the size of the population at time x = 2 (years) is f'(2) b) two-point backward difference formula, the instantaneous rate of change of the size of the population at time x = 2 (years) is f'(2) ~ c) two-point central difference formula, the instantaneous rate of change of the size of the population at time x = 2 (years) is f'(2) d) three-point central difference formula, f"(2)