Question

A rectangle is constructed with its base on the​ x-axis and two of its vertices on the parabola yequals=4949minus−xsquared2. What are the dimensions of the rectangle with the maximum​ area? What is the​ area?

Answer 1

Dimensions of rectangle : Width =
`2x` , Length =
`49 - x^2`

Area of Rectangle =
`98x - 2x^3`

Explanation:

A rectangle constructed with its base on the​ x-axis and two of its vertices on the parabola

Supposing coordinates of upper right vertex of rectangle are P =
`(x,y)`

Due to parabola symmetry, width of rectangle is twice the horizontal (X) axis distance between Y axis & point P.

Width of rectangle :
`2x`

Length of rectangle :
`y = 49 - x^2`

Area of Rectangle = Length x Width

(
`2x`) (
`49 - x^2`)

=
`98x - 2x^3`