The value of f(4) - f(3) is

Options

A. `Deltaf(2) + Delta^(2)f(1) + Delta^(3) f(1)`
B. `Deltaf(3) + Delta^(2) f(2) + Delta^(3) f(1)`
C. `Delta f(2) + Delta^(2) f(1) + Delta^(3) f(0)`
D. None of the above

Answer

A

Explanation

`f(4) - f(3) = Delta f(3)`
= `Delta [f(2) + Delta f(2)]`
`[because Delta f(2) = f(3) - f(2) ]`
`= Delta f(2) + Delta^(2) f(2)`
`= Delta f(2) + Delta^(2) [ f(1) + Delta f(1)]`
`= Delta f(2) + Delta^(2) f(1) + Delta^(3) f(1)`