Selected values of a differentiable function $f$ are shown: $f(1.9)=3.61$, $f(2)=4$, and $f(2.1)=4.41$. Using a symmetric difference quotient, the best estimate of $f'(2)$ is

Core Concept

The symmetric difference quotient is $\dfrac{f(2.1)-f(1.9)}{0.2}=\dfrac{0.8}{0.2}=4$. Averaging the left and right difference quotients gives $\dfrac{3.9+4.1}{2}=4$.