Question

Solve this problem algebraically, using your knowledge of derivatives. Do not solve by graphing.
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 1

x = length , y = width

x + 2y = 800 ... x = 800 - 2y

area = x y = y (800 - 2y) = -2 y^2 + 800 y

setting the 1st derivative equal to zero will show the max value

-4 y + 800 = 0 ... y = 200

Answer 2

You have information about the perimeter and area. Use them both.
P=w + L + w
800 = 2w + L
800 - 2w = L
Area = L(w)
Does this twig any thoughts about what you have learned?
then you will need the first and second derivatives.