Issue With Optimization Problem

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Homework Help Overview

The discussion revolves around an optimization problem involving a constraint equation, specifically y=64-x^6. Participants are exploring methods to optimize an area related to this equation.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to identify relevant equations and methods for optimization but expresses uncertainty about where to start. Some participants suggest beginning with the equations of lines through specific points and recommend creating a diagram. Others inquire about the equations used for the lines and request clarification on the original poster's attempts.

Discussion Status

The discussion is ongoing, with participants providing guidance on potential starting points and questioning the original poster's approach. There is an emphasis on understanding the setup and the equations involved, but no consensus has been reached yet.

Contextual Notes

There is a mention of integrating constants and difficulties encountered in the process, indicating potential gaps in the original poster's understanding or execution of the problem.

Guy Fieri
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Homework Statement


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Homework Equations


I have yet to figure out any relevant equations, but I do believe that the constraint equation for the optimization problem is the y=64-x^6 listed above.

The Attempt at a Solution


I am currently trying to figure out methods to begin my optimization process, such as configuring a basic area formula to optimize; however I'm not quite sure where to begin.
 

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You should start with the equations of the lines through ##AC## and ##CB##. Handle the point ##C## as if you know it: ##C=(x_0,y_0)##. Also a diagram of the situation would help you a lot. In a third step, write the integrals you must solve to calculate the area. All as if ##C## was given. At then end, after the integration, you should get a single equation in the variables ##x_0,y_0## which you can minimize.
 
fresh_42 said:
You should start with the equations of the lines through ##AC## and ##CB##. Handle the point ##C## as if you know it: ##C=(x_0,y_0)##. Also a diagram of the situation would help you a lot. In a third step, write the integrals you must solve to calculate the area. All as if ##C## was given. At then end, after the integration, you should get a single equation in the variables ##x_0,y_0## which you can minimize.
I tried doing that, but I ended up integrating constants after producing the equations.
 
Can you show us what you've done, so we can see where the difficulties lie?
This page https://www.physicsforums.com/help/latexhelp/ can help you type formulas.

Which equations did you use for the straight lines, when you've only given points?
 

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