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Ahhh, I spent SO much time on it. Figured it out (I think, anyway).
Set the 2/((1+1/x<sup>2</sup>)<sup>3/2</sup>x<sup>3</sup>) - 3/((1+1/x<sup>2</sup>)<sup>5/2</sup>x<sup>5</sup>) = 0
x = sqrt(1/2)
Point at max curvature would be [ sqrt(1/2) , ln(sqrt(1/2)) ]
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I love lamp.
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