calculus
posted by Sarah on .
A rectangle with its base on the xaxis is to be inscribed under the graph of y=2x^2. Find the height of the rectangle if the area is the largest possible area. (Round to the nearest hundreth)

Let the point of contact of the rectangle in the first quadrant be (x,y)
then the base of the rectangle is 2x and the height is y
Area = 2xy
= 2x(2x^2)
= 4x  2x^3
d(Area)/dx = 4  6x^2
= 0 for a max of Area
6x^2 = 4
x^2 = 4/6
x = ±2/6
then height = y = 2  4/6 = 4/3
= 1.33 to the nearest hundreth