You have 6L feet of fence to make a rectangular vegetable garden alongside the wall of your house, where L is a positive constant. The wall of the house bounds one side of the vegetable garden. What is the largest possible area for the vegetable garden

Maximum Area of A =

Where the dimensions are:

x = 3L feet

y  =

Step-by-step explanation:

Let the dimensions of the rectangular vegetable garden be: a and b.

Where the side a is parallel to the wall of the house.

The total length of fencing =6L ft

Perimeter of the rectangle=2(Length+Breadth)

However, since the wall is parallel to side a, there will be only one side of length a.

Therefore:

Perimeter of the Fence

6L=a+2b

⇒

Area of a rectangle=Length X Breadth

Then the area of the Rectangle=ab

The area of the garden in terms of a is then given as:

To find the maximum area(the vertex of the function), we need to determine the point at which the derivative of A(a) is zero.

Taking derivatives:

Setting

-2a=-6L

a= 3L ft.

Recall:

The maximum area therefore is:

probably the last option

step-by-step explanation: