Given point A on the graph of [math]f\left(x\right)=15-x^2[/math] we can define two rectangles.[br]Use the check-boxes in the applet below to discover for each of the rectangles when their area (or perimeter) is maximal\minimal.[br]Are the extrema of the two rectangles achieved in the same place (i.e for the same value of A)?[br] If so - prove, if not - explain.[br]

In the following applet investigate the previous questions on the more general function [math]f\left(x\right)=c-x^2[/math]