Answer
$-1.5$
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.
-------------
Evaluate $\displaystyle \frac{f(a+h)-f(a)}{h}$ for a=$-1$, h=$0.0001$
$\displaystyle \frac{f(-0.9999)-f(1)}{0.0001}=\frac{\frac{(-0.9999)^{2}}{4}-\frac{(-0.9999)^{3}}{3} -(\frac{1}{4}-\frac{1}{3})}{}$
...calculator...
$\approx-1.49987500333$
$\approx-1.5$
