Consider rectangles located as shown in the first quadrant and inscribed under a

Question

Consider rectangles located as shown in the first quadrant and inscribed under a decreasing curve, with the lower left hand corner at the origin and the upper right hand corner on the curve y = 8 - 2x3 Find the width, height and area of the largest such rectangle.

Enter your answers (as numbers)

The width of the rectangle is

The height of the rectangle is

The area of the rectangle is

Consider rectangles located as shown in the first quadrant and inscribed under a decreasing curve, with the lower left hand corner at the origin and the upper right hand corner on the curve y = 8 - 2x3 Find the width, height and area of the largest such rectangle. Enter your answers (as numbers) The width of the rectangle is The height of the rectangle is The area of the rectangle is

Explanation / Answer

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(8 - 2x3) = 8x-2x^4

let this be f(x)= 8x-2x^4

f'(x)=8-8x^3 =0

so x= 1

y = 6

The width of the rectangle is x = 1

The height of the rectangle is y = 6

The area of the rectangle is xy = 6

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