optimization: find coord's of max-area rectangle with....

[thegirl]

A rectangle has one side on the x-axis and two corners on the top half of a circle of radius 1 centered at the origin. Use calculus to find the maximum area of such a rectangle, what are the coordinates of its vertices?

I have drawn the picture, but I am unsure of where to go from there

 

[tkhunny]

It's a rectangle, right?

The base vertices are at (a,0) and (-a,0).
The length of the base is 2*a.
The upper vertices are at (a,sqrt(1-a^2)) and (-a,sqrt(1-a^2))
The height of the rectangle is sqrt(1-a^2)
The area of the rectangle is 2*a*sqrt(1-a^2)

Maximiza away!

What were you missing?

 

[thegirl]

for some reason I thought that it had something to do with the unit circle.

 

[tkhunny]

Where did I get the height of the rectangle?