Let L be the minimum length of a ladder that can reach over a fence of height h to a wall located a distance b behind the wall.

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(a) Use Lagrange multipliers to show that L = (h/3 + b2/3 3/2 (Figure 20). Hint: Show that the problem amounts to minimizing f(x, y) = (x + b) + (y + h) subject to y/b = h/x or xy = bh. (b) Show that the value of L is also equal to the radius of the circle with center (-b, -h) that is tangent to the graph of xy = bh. Wall y 50 0 h L X Ladder Fence L (-b, -h) -xy-bh -X