Monday

December 22, 2014

December 22, 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

**Answer this Question**

**Related Questions**

Physics - A rectangle has a length of 2d and a height of d. Each of the ...

calculus(Lab) - Well, first graph the graph of f(x)=-1/10x^2 + 3 2. We are going...

physics - A rectangle has a length of 2d and a height of d. Each of the ...

Physics - Three charges are located at the corners of a rectangle as follows: ...

physics - There are two +q charges and two -q charges on the corners of a square...

Calculus - prove that out of the rectangles under the curve = e raised to the ...

Calculus - The speed of a runner increased steadily during the first three ...

Calculus Help Please Urgent!!! - a) Estimate the area under the graph of f(x)=7+...

physics - A fly lands on one wall of a room. The lower left-hand corner of the ...

College Physics - In Fig. 21-24, the particles have charges q1 = -q2 = 400 nC ...