It's been a little while since I've done any problems like this, but I just wanted to make sure I'm on the right track.
Updated attempt:
2026-04-12 03:32:04.1775964724
Draw $-dU(x)/dx$ for $U(x)$
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your $u$ has a horizontal asymptote. so you you know the derivative should have a horizontal asymptote too. you derivative will have a positive local max and then decrease and approach zero. your derivative should look a little bit like the reflection on the $x$-axis of $u.$