Answer
$\$ 6.00$ per item
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 units of $f^{\prime}(a)$ are the same as the units of the average rate of change:
units of $f$ per unit of $x$.
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We build a table with
values for h: $10$ and $1$,
and
values for $\displaystyle \frac{C(10000+h)-C(10000)}{h}$
(average rate of change over $[10000, 10000+h]$).
The average rates seem to approach the value $6.00$,
(the additional table with smaller values for h confirms this estimate)
so our estimate for $C^{\prime}(10,000)$ (instantaneous rate) is
$\$ 6.00$ per item
