Let A(x) be the area of the rectangle inscribed under the curve with vertices at (-x,0) and (x,0), .

a) Find A(1).

b) What is the greatest value of A(x)? Justify your answer.

c) What is the average value of A(x) on the interval ?

I obtained:

a) ;A(1)=

b) ; Since A increases on and decreases on , there is a local maximum at .

c)avg value =

I am uncertain if I have found the correct function for A(x).