calculus
posted by tiffany on .
1.Ruth has 240 feet of fencing available to enclose a rectangular field. Express the area A of the rectangular field as a function x, where x is the length of the field.
2. For what value of x is the area largest?
3. What is the maximum area?

let the length be x
let the width be w
but 2x + 2w = 240
x + w = 120
w = 120x
area = xw = x(120x)
= x^2 + 120x
d(area)/dx = 2x + 120
= 0 for a max of area
2x = 120
x = 60
then w = 12060 = 60
for the max area the rectangle should be a square of 60 ft by 60 ft
for a max area of 3600 ft^2