Mathematics

Problem

Values of a differentiable function

g

are recorded every

0.2

units of

x

x=a-0.2

x=a

, and

x=a+0.2

. Which of the following estimation schemes is most likely to yield the smallest truncation error when approximating

g'(a)

? a)

\dfrac{g(a+0.2)-g(a-0.2)}{0.2}

\dfrac{g(a+0.2)-g(a-0.2)}{0.4}

\dfrac{g(a+0.2)-2g(a)+g(a-0.2)}{0.2}

\dfrac{g(a+0.2)-g(a)}{0.2}