Answer
$-\$ 12$ per day
Work Step by Step
The derivative, or instantaneous rate of change of $f(x)$ at $x=a$ is defined as
$f^{\prime}(a)=\displaystyle \lim_{h\rightarrow 0}\frac{f(a+h)-f(a)}{h},\ \ \ \ $(*) if the limit exists.
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: 1, 0.1. 0.01 and
values for $\displaystyle \frac{R(3+h)-R(3)}{h}$ (average rate of change over $[3, 3+h]$).
Then, we estimate whether the average rates approach any fixed number
(we estimate the limit (*), if it seems to exist)
The average rates seem to approach the value $-12$,
so our estimate for $R^{\prime}(3)$ (instantaneous rate) is
$-\$ 12$ per day
