Question

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?

Answer 1

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