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

Answer:

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

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

Step-by-step 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

($2x$) ($49 - x^2$)

= $98x - 2x^3$