# Math Help - optimization problem

1. ## optimization problem

Determine the area of the largerst rectangle that can be inscribed in a right cemicircle with a radius of 10 units. Place the length of the rectangle along the diameter.

2. Originally Posted by anna12345
Determine the area of the largerst rectangle that can be inscribed in a right cemicircle with a radius of 10 units. Place the length of the rectangle along the diameter.
$x^2 + y^2 = 100$ since the point is located on the circle
The area is $A = (2x) * y = 2xy$
Substitute into the area function so it depends on x or y, only. Then differentiate the area function to find either $dA/dx$ or $dA/dy$. Then solve for critical numbers. You may want to verify that your solution is a max (and not a min) using one of the derivative tests.