Farmer has 2,400 feet of fencing and wants to fence off a rectangular field that borders a straight river. he needs no fence along the river. write the function that will produce the largest area if x is the short side of the rectangle.

Let each side perpendicular to the river be "x".

Then the side parallel to the river is "2400-2x".

The function would be:

A (x) = x (2400-2x)

And it would be: A (x) = 2400x - 2x^2

To solve the equation:

You have a quadratic with a = - 2 and b = 2400

Maximum Area happens where:

x = - b/2a

= - 2400 / (2*-2)

= 600 ft. (width)

To find the length it will be:

= 2400-2x = 2400-2*600 = 1200 (length)