Quote of the Day:
"Philosophy is a game with objectives and no rules. 
 Mathematics is a game with rules and no objectives."

Objectives:
The student will learn to solve applied maximum minimum  
  problems.

1. Quiz on Applied Max/Min Problems.

2. Study the following example:
     Determine the point on the curve y = x^2 that is
     closest to the point (18, 0).
    
     Draw diagram:

3. Study this example:  
    The Winchester Bottling Company wants to make liter
    size soda cans; that is, they want to make cylindrical 
    cans that will hold one liter (1000 cubic centimeters) 
    of soda.  Being ecology and economy minded, the company 
    wants to use a minimum amount of material.  What 
    dimensions will enable the use of minimum material?

    What are we trying to maximize or minimize?
      We are trying to minimize surface area.
      So we need the formula for the surface area of a 
      cylinder.

     Our solution means that the optimal soda can that
     holds a liter of soda will have a radius of 5.4 cm 
     and a height of 10.8 cm.  This can would be rather 
     squat and square-looking since its diameter and 
     height are the same. (For reference, a 12-ounce soda
     can has radius of approximately 3 cm and height of 
     about 12 cm.)

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