Answer
$\displaystyle \frac{1}{3}$
Work Step by Step
We can calculate an approximate value of $f^{\prime}(a)$ by using the formula
$f^{\prime}(a)\displaystyle \approx\frac{f(a+h)-f(a)}{h}$
(Rate of change over $[a,\ a+h]$ with a small value of $h$. )
The value $h=0$.0001 works for most examples we encounter.
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Evaluate $\displaystyle \frac{f(a+h)-f(a)}{h}$ for a=$-3$, h=0.0001
$\displaystyle \frac{f(2.9999)-f(-3)}{0.0001}=\frac{\frac{-2.9999}{3}-1-(\frac{-3}{3}-1)}{0.0001}$
...calculator...
$\approx$0.333333333336$\displaystyle \approx\frac{1}{3}$
