Marquise has 200 meters of fencing to build a rectangular garden. the garden's area (in square meters) as a function of the garden's width w w (in meters) is modeled by: a ( w ) = − w 2 + 1 0 0 w a(w)=−w 2 +100w what side width will produce the maximum garden area? meters

50 m

Step-by-step explanation:

We are given that

Width of garden =w

Perimeter of rectangular garden=200 m

We know that

Perimeter of rectangle=

Area of garden

We have to find the side width that will produce the maximum garden area.

Differentiate w.r.t w

Substitute

Again differentiate w.r.t w

Hence, the garden area is maximum at w=50 m

Therefore, width of rectangular garden=50 m