K A campground owner has 2200 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. River (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) [(x)= 2200-2x (b) A(x) = (2200 -2x)x (c) First write the expression for the derivative used to find the x value that maximizes area. dA dx -= -4x+2200 The x-value leading to the maximum area is m2