Posted by sonia on Wednesday, November 21, 2012 at 10:21pm.
draw a diagram. If the foot of the ladder is x feet from the fence, and the ladder reaches y feet up the wall, then we have
x/5 = (x+3)/y
y = 5 + 15/x
if the length of the ladder is z,
z^2 = (x+3)^2 + y^2
= (x+3)^2 + (5 + 15/x)^2
z = √((x+3)^2 + (5 + 15/x)^2)
dz/dx = (x+3)(x^3-75) / <a bunch of nonzero junk>
so, dz/dx=0 at x = -3 or ∛75
z^2 = (3+∛75)^2 + (5+15/∛75)^2
z = 11.19 feet
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