When a small change in $x$ produces a large change in the value of a function $f(x)$, we say that the function is relatively sensitive to changes in $x$. The derivative $f^{\prime}(x)$ is a measure of this sensitivity $f$ has to changes in $x$. $ \begin{array}{lll}\hline & {\text { True }} & \text { Estimated } \\ \hline \text { Absolute change } & \Delta f=f(a+d x)-f(a) & d f=f^{\prime}(a) d x \\ \text { Relative change } & \frac{\Delta f}{f(a)} & \frac{d f}{f(a)} \\ \text { Percentage change } & \frac{\Delta f}{f(a)} \times 100 & \frac{d f}{f(a)} \times 100 \\ \hline\end{array} $