### Derivative problems

Prob. 2. The area of a rectangle (x,y) is the product xy. The perimeter of a rectangle P is 2x+2y. For a given P, find x and y that gives the largest area of a rectangle (x,y) for given perimeter P. Hint: Maximize A(x) = xy, where y = (P-2x)/2. Prob. 3. Find the 1st derivative of f(x) = [(3 - x^(2/3))][(x^(2/3) + 2)^(1/2