A rectangle has one side on the x-axis and two vertices on the curve y = 3 / (4 + x2). Find the vertices of the rectangle with maximum area.

Question

A rectangle has one side on the x-axis and two vertices on the curve

y = 3 / (4 + x²)

Find the vertices of the rectangle with maximum area.

Vertices =

Answer 1

The curve in this problem is symmetric with respect to the y axis.

The rectangle will be composed of 2 rectangles so it suffices to maximize the area of the

rectangle in the first quadrant.

A = x[3/(4+x²)]

The numerator of dA/dx when set = 0= 4-x².

Therefore, maximum area occurs when x=2 and the vertices required are (2,3/8) and (-2,3/8)

and (-2,0) and (2,0).