Math 124 Section 4 Fall 98 - Quiz 4

1) (4 points) Let P(x) be the profit (in dollars) from manufacturing and selling x family cars. If P(200) = 30000 and P'(200)=400, then the profit from manufacturing and selling 198 cars is approximately

(a) (b) 29200 (c) 29600 (d) 30000 (e) 30400 (f) 30800
(g) 31000

Answer: (b) P(198) is approaximately equal to

2) (6 points) A ball is thrown up into the air. The distance from the ground after t seconds is feet.

i) (2 points) The velocity of the ball after 2 seconds is:

(a) 0   (b) -16   (c) 16   (d) 32   (e) 64   (f) 80   (g) 96   (h) 128

Answer: (d) The velocity is the derivative of the distance function which is s'(t) = 96 - 32t. Hence, the velocity after 2 seconds is s'(2)= 96 - 64 = 32.

ii) (2 points) The average velocity during the first two seconds is

(a) s(2)   (b) s'(2)   (c) s''(2)   (d)   (e)

Answer: (e) By definition, the average velocity is the distance traveled divided by the time traveled.

iii) (2 points) The acceleration after 2 seconds is

(a) -32   (b) -16   (c) 0   (d) 16   (e) 32   (f) 64   (g) 96

Answer: (a) The acceleration a(t) is the second derivative of the distance function. Hence a(t) = s''(t) = -32. It happens to be a constant function. In particular, a(2) = -32.