Shenelle has 100100100 meters of fencing to build a rectangular garden. The garden's area (in square meters) as a function of the garden's width xxx (in meters) is modeled by: A(x )= -(x-25)^2 + 625

25metres

Step-by-step explanation:

Complete question

Shenelle 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 xxx (in meters) is modeled by: A(x )= -(x-25)² + 625

What width will produce the maximum garden area?

At maximum area of the garden dA/dx = 0

dA/dx = -2(x-25)

0 =-2(x-25)

-2(x-25) = 0

x - 25 =0

x = 0+25

x = 25

Hence the width that will produce the maximum garden area is 25metres

625  square meters

Step-by-step explanation:

The garden's area is modeled by a quadratic function, whose graph is a parabola.

The maximum area is reached at the vertex.  

So in order to find the maximum area, we need to find the vertex's y-coordinate.  

The function A(x)  is given in vertex form.

The vertex of -(x-25)^2+625 is at (25,625)  

In conclusion, the maximum garden area is 625square meters.

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