Does there exist a continuous function that changes sign and monotonicity at the same point? [closed]

I'm looking for a function with the following properties, and I'm wondering whether such a function exists. Let $I$ be an open interval, and let $c \in I $ be a point within that interval. I would like to find a function $f: I \to \mathbb{R} $ such that:

1. Continuity: $𝑓$ is continuous on the entire interval $I$
2. Zero at $𝑐$: $f(c)=0$
3. Sign Change at $c$: $f$ changes sign at $𝑐$
4. Monotonicity Change at $𝑐$: $f$ changes monotonicity $c$

Is it possible to construct such a function, and if so, what would an example look like? If not, why does such a function not exist?

Any insights would be appreciated.