Name: ______________________
Final Exam
Take home portion. Please show all work. This is a calculus test, so I need to see calculus work. If you
use a calculator to evaluate an integral, you need to show it set up.
1. Nonbuoyant bulls and cows need to be pastured separately on a field bounded by a river. (The cattle
don't swim, so there doesn't need to be any fence on the river side.) The rancher has 5000 yards of
fencing. What dimensions will maximize the pasturage available for the animals?
2. On stage, a light is being lowered at a rate of half a foot per second, 5 feet away from a 6 foot tall
actor. How fast is that actor's shadow growing when the light is 10 feet off the ground?
(Hint: Use similar triangles to set this up. The Pythagorean Theorem isn't going to be very helpful.
Also, it will be easiest to work with if you separate the variables—put the separate variables on
different sides of the equation.(Otherwise, you'll have to use implicit differentiation to take the
derivative of the equation with both variables in it. On the other hand, clearing the denominator will
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 Spring '08
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 Calculus, Continuous function, maximum error, higher marginal productivity, CobbDouglas productivity function

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