1 / 6

A Classic Problem

There must be a local maximum here, since the endpoints are minimums. A Classic Problem. You have 40 feet of fence to enclose a rectangular garden along the side of a barn. What is the maximum area that you can enclose?. A Classic Problem.

zuwena
Download Presentation

A Classic Problem

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. There must be a local maximum here, since the endpoints are minimums. A Classic Problem You have 40 feet of fence to enclose a rectangular garden along the side of a barn. What is the maximum area that you can enclose?

  2. A Classic Problem You have 40 feet of fence to enclose a rectangular garden along the side of a barn. What is the maximum area that you can enclose?

  3. 1 Write it in terms of one variable. 2 Find the first derivative and set it equal to zero. 3 Check the end points if necessary. To find the maximum (or minimum) value of a function:

  4. Example 5: What dimensions for a one liter cylindrical can will use the least amount of material? Motor Oil We can minimize the material by minimizing the area. We need another equation that relates r and h: area of ends lateral area

  5. Example 5: What dimensions for a one liter cylindrical can will use the least amount of material? area of ends lateral area

  6. Notes: If the function that you want to optimize has more than one variable, use substitution to rewrite the function. If you are not sure that the extreme you’ve found is a maximum or a minimum, you have to check. If the end points could be the maximum or minimum, you have to check. p

More Related