A farmer with 2000 meters of fencing wants to enclose a rectangular plot that borders on a straight river. if the farmer does not fence the side along the river, what is the largest area that can be enclosed?

The area is given by x (2000 - 2x) where x is the width of the rectangular plot.

dA/dx = 2000 - 4x = 0 (for maximum / minimum area)

4x = 2000

x = 500

and the length of the plot = 2000 - 2 (500) = 1000

d^2y/dx^2 is negative so its a maximum area

Maximum area = 1000*500 = 500,000 m^2