Mathematics

Problem

The differentiable function

g

is defined for all real numbers, and

g'(5)

exists. Which of the following difference quotients is most likely to give the best numerical approximation of

g'(5)

? a)

\dfrac{g(5.1)-g(4.9)}{0.2}

\dfrac{g(5.001)-g(5)}{0.001}

\dfrac{g(6)-g(5)}{1}

\dfrac{g(5)-g(4)}{1}