Math 1A – Chapter 4.1 – 4.4 Test – Fall ’04       Name__________________________

Show your work for credit.  Write all responses on separate paper.

 

1.      A falcon flies up from its trainer at an angle of 60◦ until it has flown 200 ft.  It then levels off and continues to fly away.  If the speed of the bird is 132 ft/sec, how fast is the distance between the bird and the falconer increasing after 6 seconds?

 

2.      A ladder 19 ft long leans against a 15 foot wall so the top of the ladder juts over the top of the wall.  If the base of the ladder slides away from the wall at the rate of 3 ft/sec, find the rate at which the height of the top end of the ladder is decreasing when 2 feet of ladder projects over the wall.

 

3.      Find a formula for a function that

a.       … is continuous on  and has an absolute maximum, but no absolute minimum.

b.      …is discontinuous on  but achieves both an absolute maximum and an absolute minimum.

4.      Consider .

a.       Use a graph to estimate where the absolute maximum and minimum occur.

b.      Use calculus to find the exact values of these extremes.

5.      Consider

a.       Find the intervals on which x is increasing or decreasing.

b.      Find the local maximum and minimum values of x.

c.       Find the intervals of concavity and the inflection point.

6.      Find values of a and b so that  has an absolute maximum at .

7.      Consider the curve defined parametrically by   where .

a.       For what values of t does the curve have vertical tangent lines?

b.      For what values of t does the curve have horizontal tangent lines?