Name: ________________
Test #3
Applications of Derivatives
Math 160
Calculators are permitted, but show all work.
1.
Solve either of the problems below.
A. A boat is tied to a dock as shown in the picture below. A winch on the dock is connected to the boat,
and when the winch is turned, the rope is drawn in, and the boat moves closer to the dock. The top of
the winch is 5 feet above the point where the rope attaches to the boat. When the winch is turned, the
rope is pulled in at a constant rate of 2 ft per second.
How fast is the boat approaching the dock when it is 12 feet away?
B. For the graph of
y
2
x
3
10
y
9
=
0
find the slope,
dy
dx
, of the tangent line.
At what point(s) does this graph have a horizontal tangent?
At what point(s) does this graph have a vertical tangent?
5 ft.
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2. A fence is to be built to encolse a rectangular area of 800 square feet. The fence along three sides is
to be made of material that costs $6 per foot. The material for the fourth side costs $18 per foot. Find
the dimensions of the rectangle that will allow for the most economical fence to be built (i.e, the fence
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 Spring '08
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 Derivative, Mathematical analysis, $6, $18, minimum value

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