Math 181

Quiz 5

July 16, 2013 Name:
__ Key __

1. A kite flies at a height of 40 feet. When the kite is at a horizontal distance of 30 feet from the kid flying it, a wind blows it at a (horizontal) speed of 10 feet/second away from kid. At what rate does the kid need to let out more string (or, in other words, at what rate is the distance between the kite and the kid increasing)?

*If we let x be the horizontal distance of the kite from the kid, and *

*z** be the length of the string, then *

*Since initially x=30, we get z=50.*

*Differentiating, *

2. For the function :

a. Find the critical points

*are** the only critical
points.*

b. Find the absolute maximum and minimum on the domain [-3,5]

*Check the critical
points and the endpoints:*

*So, on this domain the
absolute maximum is 60 at x=5, and the absolute minimum is -21 at x=2.*