SOLVING

[twins12]

The base of a rectangle lies on the -axis, while the upper two vertices lie on the parabola y=7-x^2. Suppose that the coordinates of the upper right vertex of the rectangle are . Express the area of the rectangle as a function of .
Answer__________


This is what I have so far

area of a rectangle= L*W or X*Y

A=x*y
= x*(7-x^2)
= 7x-x^3
But I got it wrong.

 

[arthur ohlsten]

y=7-x^2 parabola.open down vertex at 0,7

let upper right rectangle vertex be at x= A and on the parabola
coordinates of upper right vertex A,7-A^2
coordinates of upper left vertex, -A,7-A^2

rectangle width=2A
rectangle height=7-A^2

area of rectangle=2A[7-A^2] 0<A<7
max area at A= [sqrt 21] / 3

Arthur