What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y=12-x^2?

Question

anonymous · Answer

Make a quick sketch of the figure. You have an up-side-down parabola translated up and you are fitting a rectangle in this small space. Since the parabola is an even function note that the base of the rectangle will be 2x. You also have the function for the height. So develop an equation for the area and maximize it.

anonymous · Answer

Area of rectangle: LxW so (2x)(y)=2x(12-X^2) then I would solve for x and substitute it back into the Area equation

anonymous · Answer

?

dumbcow · Answer

that is your area equation
A =2x(12-x^2)
maximize by differentiating and settting equal to 0
then solve for x

anonymous · Answer

Okay thanks!