Diana has available 480 yards of fencing and wishes to enclo

Diana has available 480 yards of fencing and wishes to enclose a rectangular area Express the area A of the rectangle as a function of the width W of the rectangle for what value of W is the area largest? What is the maximum area? A(W) =

Solution

Dear Student Thank you for using Chegg Total Length of fencing available = 480 yards Width of rectangular area = W Let length of rectangular area = L Perimeter of rectangular area = 2(L + W) 2( L + W) = 480 L = 240 - W a) Area (A) = L * W = (240 - W) W = 240W - W^2 b) Value of W for which Area is largest Differenciate Area w.r.t. W dA/dW = 240 - 2W = 0 W = 120 L = 240 - W = 240 -120 = 120 yards Now double differenciating A in order toensure that if the result is negative then the area corresponding to L =120, W = 120 is the maximum area d2A/dW2 = -2 Hence W = 120 corresponds to maimum area of rectangle c) Maximum area = L * W = 120 * 120 = 14400 yard^2 Solution