APFIVE Average Value of a Rate Function
A function $$v(t)$$ gives the rate of change of inventory in a warehouse, in items per hour, where $$t$$ is measured in hours since 8 A.M. Positive values indicate items being added to inventory, and negative values indicate items being removed. Which of the following gives the meaning of
$$\frac{1}{11-4}\int_4^{11} v(t)\, dt$$
in the context described?
A
The total number of items that were processed (added or removed) between 12 P.M. and 7 P.M.
B
The net change in inventory, in items, between 12 P.M. and 7 P.M.
C
The instantaneous rate of inventory change, in items per hour, at 7 P.M.
D
The average rate of inventory change, in items per hour, between 12 P.M. and 7 P.M.
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