optimization: first quadrant with one vertex at the origin

[wind]

Hi, can someone help me with this question?

A rectangle lies in the first quadrant with one vertex at the origin and two of the sides along the coordinate axis. The fourth vertex lies on the parabola y=27-x^2. Find the maximum area of the rectangle and explain why it is a maximum.

so, we need to find a relation ship between all the variables, right?

from the equation of the parabola, the lenght of the rectangle is 27.

a=Lw

...thats all I can think of doing...

Thanks

 

[skeeter]

the area of the rectangle is A = xy = x(27 - x²)

find dA/dx and maximize.