Posted by Anonymous on Thursday, October 27, 2011 at 1:48pm.
A rectangle is inscribed with its base on the x axis and its upper corners on the parabola
y= 11x^2.
What are the dimensions of such a rectangle with the greatest possible area?

Calculus  Steve, Thursday, October 27, 2011 at 4:16pm
The area of the rectangle with corners (x,0), (x,0) (x,y) (x,y) is
a = 2x * (11x^2)
a = 22x  2x^3
da/dx = 22  6x^2
da/dx = 0 when x = √(11/3)
So, the rectangle is 2√(11/3) x 22/3 with area 44/3 * √(11/3) = 28.08