Answer
$-2$
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=2, h=0.0001
$\displaystyle \frac{f(2.0001)-f(2)}{0.0001}=\frac{1-2(2.0001)-(1-2(2))}{0.0001}$
$=\displaystyle \frac{-0.0002}{0.0001}=-2$
