A rectangle is inscribed between the X axis and the parabola y=36-x^2. One side of the rectangle falls on X axis

Question

Need to write a function for the area, A of the rectangle  in terms of x.

Length and width that yield maximum  area.

Find max area  

Answer 1

2x represents the base of the rectangle

-x² + 36 represents the height of the rectangle

A = 2x(-x² + 36)

A = -2x³ + 72x

A' = -6x² + 72

0 = -6x² + 72

6x² = 72

x² = 12

x = 2√3

Base should be at (-2√3, 0) and (2√3, 0)