Activity 3.4.4. consider the region in the x-y plane that is bounded by the x-axis and the function f (x) 25 − x 2 . construct a rectangle whose base lies on the x-axis and is centered at the origin, and whose sides extend vertically until they intersect the curve y 25 − x 2 . which such rectangle has the maximum possible area? which such rectangle has the greatest perimeter? which has the greatest combined perimeter and area? (challenge: answer the same questions in terms of positive parameters a and b for the function f (x) b − ax2 .)