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

Answer:

A_max =  11250 ft^2

Step-by-step 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:

$\frac{dA}{dx}=\frac{d}{dx}[300x-2x^2]=300-4x$    (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