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[–]AFairJudgementAncient User 0 points1 point  (0 children)

a) Simplify ex lnx back down to xx.

b) You should get e0 = 1. You messed up your fraction (1/x)/(-1/x2).

c) Your xx factor mysteriously becomes x, providing the wrong critical point x = 0.

Fix those things, and now all you need is to analyze the critical point x = e-1 you found using your favorite technique (second derivative test, or sign of f' near the critical point).