Hello, symmetry!

Did you make a sketch?

Jack has 3000 feet of fencing available to enclose a rectangular field.

One side of the field lies along a river, so only 3 sides require fencing.

(a) Express the area of the rectangle as a function of ,

where is the length of the side parallel to the river.

(b) Graph . .For what value of is the area largest?The area of the field is: .Code:~ + ~ ~ ~ ~ ~ ~ + ~ | | y| |y | | * - - - - - - * x[1]

The total fencing is: .

Since Jack has 3000 feet of fencing: .[2]

Substitute[2]into[1]: .(a)

If we graph , it looks like this:The maximum occurs when .Code:| | * | * : * | * : * | * : * |* : * | : --*-----------+-----------*-- | 1500 3000