If 800 feet of fencing is used to enclose a rectangular plot of land that borders a river, what is the maximum area that can be enclosed? Answer to the nearest square foot without commas. For example, if the answer is 1,000, write 1000.

P + 2 q = 800 so p = 800 - 2 q A = p q = (800 - 2q) q A = - 2 q^2 + 800 q now you could find the vertex of this parabola easily with Algebra 2 by completing the square but you said calculus so dA/dq = 0 at max = - 4 q + 800 or q = 200 then p = 800 - 400 = 400 so A = 80,000 ft^2 or about two acres