A campground owner has 1300 m of fencing. He wants to enclose a rectangular field bordering a river, with no fencing along the river. (See the sketch.) Let x represent the width of the field. (a) Write an expression for the length of the field as a function of x. (b) Find the area of the field (area = length x width) as a function of x. (c) Find the value of x leading to the maximum area. (d) Find the maximum area. (a) f(x)=1,300-2x (b) A(x)=1,300x - 2x (c) First write the expression for the derivative used to find the x value that maximizes area. dA dx = 1,300-4x The x-value leading to the maximum area is 325 m. m (d) The maximum area of the rectangular plot is 211,250 m