$\frac{\sin x}{x}$ at $x = 0$ should be a good example.

P.S.: Talking about esoteric definitions, if you can introduce stationary point without derivatives, you can then introduce derivatives using sheaves, like you would introduce vectors on a smooth manifold. It would broaden the consciousness of your freshmen, he-he ^_^

$\frac{\sin x}{x}$ at $x = 0$ should be a good example.