How Can You Optimize Fence Length Without Using Derivatives?

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SUMMARY

The discussion focuses on optimizing the area enclosed by a fixed length of fence, specifically 500 meters, without using calculus or derivatives. Participants suggest using a quadratic function to represent the area and finding its vertex to determine the maximum area. Graphing the function is also recommended as a viable method for visualizing the optimization problem. The conversation highlights alternative approaches to optimization that do not rely on advanced calculus techniques.

PREREQUISITES
  • Understanding of quadratic functions
  • Basic knowledge of graphing techniques
  • Familiarity with the concept of vertices in parabolas
  • Knowledge of optimization principles in mathematics
NEXT STEPS
  • Study how to graph quadratic functions effectively
  • Learn about finding the vertex of a parabola
  • Explore optimization techniques without calculus
  • Research practical applications of quadratic optimization in real-world scenarios
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High school students, educators in mathematics, and anyone interested in learning optimization techniques without advanced calculus.

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Hey guys this isn't exactly a homework question. I'm helping my girlfriend with her grade 12 college level math course. When i was in grade 12 i took calculus.. and she called me and asked for help with optimization. I don't think in her class they are learning about calculus so how would you go about say optimizing 500m of fence for the greatest area without using derivatives?

Derivatives is the only method i know of to do these types of problems... unless she is supposed to trial and error?
 
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By graphing the function that gives the area of the enclosed area. Because of the length constraint, I think you'll be getting a quadratic function whose vertex can be found without the use of calculus.
 
true enough, i never thought about it that way how dumb of me lol :P thanks mark44
 

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