She Elle has 100 meters of fencing to build a rectangular garden. The garden's area (in square meters) as a function of the garden's width "w" (in meters) is modeled by: A(w) = -(w-25)^2+625 What is the maximum area possible in square meters?

Step-by-step explanation:

In this problem, we are told that the area of the garden is given by the expression

where

w is the width of the garden (in meters)

Here we want to find the maximum possible area.

The maximum of a function f(x) can be found by requiring that its first derivative is zero:

Therefore, here we have to calculate the derivative of and find the value of w for which it is equal to zero.

Let's start by rewriting the area function as

Now we calculate the derivative with respect to w:

Now we require this derivative to be zero, so

So now we can substitute this value of w into the expression of A(w) to find the maximum possible area:

This value is allowed because we know that the maximum length of the perimeter of the fence is 100 meters; If the garden has a square shape, the length of each side is , and the area of the squared garden is

Which is equal to what we found earlier: this means that the maximum area is achieved if the garden has a squared shape.

1 x=22.52

2: 65/39=604+39x

65x-39x=604

26x=604

x=604/26

×=23.23