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September 15, 2014

September 15, 2014

Posted by **Anonymous** on Wednesday, April 11, 2007 at 9:50pm.

y = sqrt(9 - x2)

Find the width, height and area of the largest such rectangle.

let the top right vertex of the rectangle which is on the curve by (x,y)

x is the width of the rectangle, y is the height

then the area = xy

=x√(9-x^2)

differentiate using the product rule, set the derivative equal to zero and solve for x.

or....

we could use common sense, notice that your given equation when squared and rearranged is really part of a circle with centre at the origin and radius 3.

So the largest rectangle would be where the x equals the y, namely when x = 3/√2

(which is what you get if you do it by Calculus as I decribed above.

So the area = (3/√2)^2 = 9/2

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