Question

A family with three young children just moved into a house with a yard that is not fenced in. The previous owner gave them

300 feet of fencing to use to enclose part of their backyard. Use the quadratic function A(2) = x(300 - 2x) to determine

the maximum area of the fenced-in yard.

Answer 1

A_max = 11250 ft^2

Explanation:

You have the following function for the area of the backyard:

`A=x(300-2x)=300x-2x^2` (1)

To find the maximum area, you first derivative the function A respect to x:

`(dA)/(dx)=(d)/(dx)[300x-2x^2]=300-4x` (2)

Next, you equal the function (2) to zero in order to obtain the value of x:

`300-4x=0\\\\x=75`

Finally, you replace the value of x=75 in the function A in (1):

`A=(75)(300-2(75))=11250\ ft^2`

hence, the maximum area is 11250 ft^2