Need help with review question on test tomorow

[2Pac]

need help please. tonight if possible. I need to find the largest area of a rectangle with base on the x-axis and upper corners touch the parabola with the equation y=12-x^2
:smile: thanks :smile:

[AKG]

Well, you know the rectangle will be symmetrical about the y-axis. That means, if it touches the parabola at x = -a, it will touch at x = a as well. The rectangle will have an area of A = bh = (2x)(12 - x^2). Hopefully you see why this is. Now, it's simply a matter of finding the x value which gives a maximum for A, and I'm sure you know how to do this.