Expert: Paul Klarreich - 12/14/2008

Question
A rectangle ABCD with sides parallel to the coordinate axes is inscribed in the region enclosed by the graph of y=-4x^2+4 and the x-axis. Find the x- and y-coordinates of C so that the area of the rectangle ABCD is a maximum.

i used the distance equation and got 16x^4-31x^2t16, then i took the derivative--64x^2-62x, and i got x=0 or the sqaure root of 31/32, i plugged the sqaure root of 31/32 into y=-4x^2+4 and got 1/8


Answer
Questioner:   Kathleen
Category:  Calculus
Private:  No
 
Subject:  AP Calculus-max and min
Question:  A rectangle ABCD with sides parallel to the coordinate axes is inscribed in the region enclosed by the graph of y=-4x^2+4 and the x-axis. Find the x- and y-coordinates of C so that the area of the rectangle ABCD is a maximum.

i used the distance equation and got 16x^4-31x^2t16, then i took the derivative--64x^2-62x, and i got x=0 or the sqaure root of 31/32, i plugged the sqaure root of 31/32 into y=-4x^2+4 and got 1/8
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Hi, Kathleen,

Your base will be on the x-axis, so you just need to find the x-coordinate on the right.

The base is  2x.
The height is y = -4x^2 + 4
The area A = 2xy.

Now just plug in:

A = 2x(-4x^2 + 4) = -8x^3 + 2x

No distance formula. Just the usual stuff.

You should be able to take it from here.