maximizing the area of a rectangle inscribed in a parabola

**yeloc** · September 28th 2009, 04:24 PM

A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=9-[(x^2)/4] . What are the dimensions of such a rectangle with the greatest possible area?

I found the height to be 6, but I cannot figure out the width.

**skeeter** · September 28th 2009, 05:00 PM

Originally Posted by yeloc

A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=9-[(x^2)/4] . What are the dimensions of such a rectangle with the greatest possible area?

I found the height to be 6, but I cannot figure out the width.

$A = 2xy$

$A = 2x\left(9 - \frac{x^2}{4}\right)$

find $\frac{dA}{dx}$ and determine the value of $x$ that maximizes $A$ .

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