M2 differentiation

1. A rectangle is inscribed in a triangle enclosed by the coordinate axes and the line passing through (0,2) and (3,0). Find the greatest possible area for the rectangle.

2. Find the area of the largest rectangle that can be inscribed in the curve (x^2)/16 + (y^2)/9 = 1.

3. Two ships are sailing straight away from the point O. The routes of the two ships is at an angle of 120 degrees with each other. Ship A moves at 20km/h and ship B moves at 15km/h. At what rate are the ships moving apart from each other when OA = 4km and OB = 3km?