Optimization of Area; Inscribed Rectangles

[Qube]

Homework Statement

http://i.minus.com/jbkHm5oH1LfQ1k.png

Homework Equations

The area of a rectangle is its base times its height.

The Attempt at a Solution

The rectangle is inscribed. Its area is 2xy. I can substitute in the equation of the semicircle to get rid of the y-term in my area equation. I can then differentiate with respect to x and find what zeros the derivative (or causes the derivative not to exist) and test the points I find that are on the domain of x (0 to square root of 12).

I find x = sqrt6 as that point that maximizes area and therefore the dimensions must be 2sqrt6 and sqrt6.

http://i.minus.com/jFWGaWoQsb5FX.jpg

 

[jbunniii]

Looks right to me.