How Can You Optimize Fence Length Without Using Derivatives?

AI Thread Summary
To optimize the area enclosed by 500 meters of fencing without using derivatives, one can utilize the properties of a quadratic function. The area can be expressed as a function of the dimensions of the fence, leading to a parabolic equation. By identifying the vertex of this parabola, which represents the maximum area, the optimal dimensions can be determined. Graphing the function can also visually demonstrate the maximum area achievable. This approach allows for effective optimization without requiring 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
 

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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