AP Calculus	                              Review for Test 7
Related Rates
1.	A ladder 25 feet long is falling down a building at the rate of  ft/sec.  At the time the foot of the ladder is 24 feet from the building, how fast is the bottom of the ladder moving away from the building?

2.	If ƒ(x) = x2 – 7x + 6 is a function, would you be using just the Mean Value Theorem or also Rolle’s Theorem when you   sought the elusive “c” on the interval [1,6]?   Find the “c”.    

3.	If  ƒ(x)  =   find  k  so that ƒ(x) will be continuous at  x = 1.  		

4..	If  ƒ(x)  =  sin(x7),  then  ƒ ‘ (x)  =        				
5.	Find the rate of change of the surface of a sphere at the time its volume is ft3 and its radius is increasing  at   the rate of  ft/sec.  
6.	A water tank has the shape of an inverted cone with altitude of 18 ft. and base radius of 9 ft.  If water is pumped in at 12 ft3/min, how fast is the water level rising when the water is 4 ft. deep?
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7.         
8.         If the derivative of the function  is a constant.  Find n.

9.              Find b to make the function continuous at x = 3

10.       A stone is thrown into a pool of water.  Circular ripples radiate from the disturbance on the surface such that the radius is increasing at a rate of .  Find the rate of change in the area of the largest circle when its radius is 9 inches.  

11.       If    and   when y = 3 and .    Find .  

Answers:  1.  	2.  Rolle’s :   c = 	3.  	4. 7x6cos  5.  8π ft2/sec   
6.     7.      8.  n = 5      9.  b = -1     10.       11.