Quote of the Day: 
"The calculus is the greatest aid we have to the 
   application of physical truth in the broadest sense 
   of the word." -- W. F. Osgood

Objectives:
The student will solve related rates problems.
       
1. Bell Ringer.  

2. Related rates problems involve two rates which are
   related to each other.  How do you find instantaneous 
   rate?  
   Answer: By taking the derivative with respect to time.

3. Example:
     An off-shore tanker begins leaking oil so that the
     radius of the circle is changing at the rate 
     of 2 miles/hour. How fast is the area of the oil 
     spill changing when the radius is 6miles?

4. Strategy for solving related rates problems
  (1) Draw and label a diagram.
  (2) Write down what you wish to solve for (express it in
      terms of a variable). e.g., dh/dt
  (3) Identify other variables in the problem.
  (4) Write equations that relate the variables.
  (5) Use substitution to obtain one equation involving the 
      known quantities.
  (6) Take the derivative of each side with respect to 
      time.
  (7) Solve for the desired rate.
  (8) Make numerical substitutions.


5. Example: Ladder Problem
     Draw this on the blackboard and show that the rates 
     are not the same.

     A 26-foot ladder is leaning against a wall.  If it is 
     being pulled away from the wall at a rate of 4 ft/sec,
     How fast is the top of the ladder sliding down the
     wall when the foot of the ladder is 10 feet from the 
     wall?

     Answer:  -5/3 ft/sec

   Example: Kite Problem
     A kite is at an altitude of 75 feet and moving
     horizontally at 12 ft/sec.  How fast is the string 
     being paid out when the kite is 100 feet away 
     (measured along the string)?

     Answer is 7.94 ft/sec

6. Assignment: 
      Read p. 217 - 220 

            p. 221 (1a, 7, 10, 13, 15, 17)  

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