I'm trying to determine the maximum area in a specific ellipse that can be filled with any 3 (horizontally aligned) rectangles. $Ellipse: \frac{x^2}{36}+\frac{y^2}{16}=1$ $Area: A=4(x_1*y_1+(x_2-x_1)*y_2)$
Here's an image:
By substituting $y_1$ and $y_2$ with a function of $x_1$ and $x_2$ (with the equation of the ellipse), differentiating that and equal it to 0, I get $x_1$ as a function of $x_2$. I don't think that's the solution, so how can I solve this? Is there even a finite number of solutions?
Hope you can/will help me :)