Question

Increasing numbers of manatees ("sea sirens") have been killed by boats off of a state's coast. The following graph shows the relationship between the number of boats registered in the state and the number of manatees killed each year.
The regression curve shown is given by
f(x) = 3.51x2 − 30.1x + 81 (4.5 ≤ x ≤ 8.5)
where x is the number of boats (hundreds of thousands) registered in the state in a particular year and f(x) is the number of manatees killed by boats in the state that year.

The graph has horizontal axis labeled "Boats (100,000)" and vertical axis labeled "Manatee deaths." The graph has a scatter plot of 24 points and a regression curve through the points. The regression curve enters the window in the first quadrant, goes up and right becoming more steep, passes through the approximate point (4.5, 17), passes through the approximate point (5, 18), passes through the approximate point (6, 27), passes through the approximate point (7, 42), passes through the approximate point (8, 65), passes through the approximate point (8.5, 79), and exits the window in the first quadrant.
(a)
Compute f '(x).
f '(x) =

What are the units of measurement of f '(x)?
100,000 boats per manatee deaths
manatee deaths per year
manatee deaths per 100,000 boats
boats per year
(b)
Is f '(x) increasing or decreasing with increasing x?
increasing
decreasing
(c)
Compute and interpret f '(8).
f '(8) =
At a level of 800,000 boats, the number of manatee deaths is increasing at a rate of

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.