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Calculus 1 Hour Exam 2 (continued) - Math 220 Fall, 2010

A farmer wishes to fence off three identical adjoining rectangular pens as in the

diagram shown, but he only has 600 feet of fencing available. Determine the values

for x and y which will maximize the total area enclosed by the three pens.

Answers: x = 50 y = 75

A small balloon is released at a point 40 feet away from an observer, who is on level

ground. If the balloon rises straight up at a rate of 10 feet per second, how fast is the

distance from the observer to the balloon increasing when the balloon is 30 feet high?

Answer: 6 ft/sec

What are the coordinates (x ,y) for the highest point on the graph of the function

g(x) = 180 x - 10 e^2x ?

Answer: ( x, y ) = ( ln 3, 180 ln 3 - 90 )

A function f(x) has first derivative f ‘ (x) = e^0.5x(10x – 60).

a. Upon which interval is f(x) increasing?

b. Upon which interval is the graph of f(x) concave down?

Answers: a. [ 6, ∞ ) b. ( - ∞ , 4 ]

10.

Determine a formula for w as a function of s so that dw/ds = 10 s and w(1) = 2.

Answer: w(s) = 5s² - 3