A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 2-x^2. What are the dimensions of such a rectangle with the great

Question

help!!! i need this answered asap 

Answer 1

Coordinates of upper right corner = (x, 2-x²)

 

Length of base = 2x

Height = 2-x²

 

A = area of rectangle = 2x(2 - x²) = 4x - 2x³ , 0 < x < √2

 

A' = 4 - 6x²

 

A' = 0 when x = √(2/3)

 

When 0 < x < √(2/3), A' > 0.  So, A is increasing

 

When √(2/3) < x < √2, A' < 0.  So, A is decreasing

 

Maximum area when x = √(2/3)

 

Dimensions:  length = 2x = 2√(2/3)

 

                    height = 2 - x² = 4/3