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.

A_max =  11250 ft^2

Step-by-step explanation:

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

  (1)

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

   (2)

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

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

hence, the maximum area is 11250 ft^2

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