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.)