Max square/rec area under the curve

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