Page 111 - Calculus Demystified

CHAPTER 3 Applications of the Derivative
98 8. A body is launched straight down at a velocity of 5 ft /sec from height
400 feet. How long will it take this body to reach the ground?
2
9. Sketch the graph of the function h(x) = x/(x − 1). Exhibit maxima,
minima, and concavity.
10. A punctured balloon, in the shape of a sphere, is losing air at the rate of
3
2 in. /sec. At the moment that the balloon has volume 36π cubic inches,
how is the radius changing?
11. A ten-pound stone and a twenty-pound stone are each dropped from height
100 feet at the same moment. Which will strike the ground first?
12. A man wants to determine how far below the surface of the earth is the
water in a well. How can he use the theory of falling bodies to do so?
13. A rectangle is to be placed in the first quadrant, with one side on the x-axis
and one side on the y-axis, so that the rectangle lies below the line 3x+5y =
15. What dimensions of the rectangle will give greatest area?
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14. A rectangular box with square base is to be constructed to hold 100 cubic
inches. The material for the base and the top costs 10 cents per square
inch and the material for the sides costs 20 cents per square inch. What
dimensions will give the most economical box? 2
2
15. Sketch the graph of the function f(x) =[x −1]/[x +1]. Exhibit maxima,
minima, and concavity.
16. On the planet Zork, the acceleration due to gravity of a falling body near the
surface of the planet is 20 ft /sec. A body is dropped from height 100 feet.
How long will it take that body to hit the surface of Zork?

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