Hi everyone, I've been working on this optimization problem for awhile now. I guess I don't understand the steps. Here's my work.

The Problem

Code:

A rectangle is inscribed with its base on the x-axis and
its upper corners on the parabola y = 4 - x^2. What are
the dimensions of such a rectangle with the
greatest possible area?

My work

Code:

Define variables...
A = 2xy
y = 4- x^2
setup problem:
A(x) = 2x ( 4 - x^2)
Find d/dx:
A'(x) = 8 - 6x^2
Critical Points:
0 = A'(x) = { -1.1547, 1.1547}
~~Then am I supposed to use this formula??? ----> 4x + 3y ?

Thanks for your time

-M