Issue With Optimization Problem

[Guy Fieri]

Homework Statement

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.

 

[fresh_42]

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.

 

[Guy Fieri]

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.

 

[fresh_42]

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?