If the farmer has 250 feet of fencing to create a rectangular pen, define a function f that expresses the area of the field (measured in square feet) as a function of the width of the side of the field w (measured in feet). What is the maximum area possible?

Answer: Maximum area possible f(max)  = 3906,25 ft²Dimensions:a  = 62,5  ftw  = 62,5 ftStep-by-step explanation:Perimeter of the rectangular fencing    P  =  250 feetAnd sides of the rectangle  a  and  w (width of rectangle)ThenA =  a*w2a  + 2w  = 250       ⇒  a  =  (250 -2w)/ 2    ⇒  a = 125 - wf(w)  =  (125  - w ) *w        f(w)  = 125w - w²  Taking derivatives both sides of the equationf´(w)   =  125  - 2w              f´(w)   = 0           125  - 2w = 0w = 125/2w = 62,5 ft            ⇒  a = 125 - 62,5 a = 62,5 ftf(max)  = ( 62,5)²f(max)  = 3906,25 ft²