Posted by jim on Tuesday, May 19, 2009 at 8:06pm.
A rectangle has its base on the xaxis and its upper two vertices on the parabola
y=12−x2 .
What is the largest area that the rectangle can have

calculus  Reiny, Tuesday, May 19, 2009 at 8:16pm
let the points of contact be (x,y) and (x,y)
so the base is 2x and the height is y
but y=12x^2
so the
Area = 2xy
= 2x(12x^2)
= 24x  2x^3
d(Area)/dx = 24  6x^2
= 0 for a max Area
solve 2x^3  24 = 0
sub that back into the Area = 2x(12x^2)