Examples of functions zero on the boundary

Question

What are examples of a function $f(x)$ satisfying $$f(0)=f(l)=f'(0)=f'(l)=0?$$

One example is $f(x)=x^{\beta_1}(l-x)^{\beta_2}$ with $\beta_1, \beta_2>1$.

Edit Not of the form $f\cdot g$ or etc.

Answer 1

What about some simple trigonometric functions? A possible example is

\begin{equation} f(x) = \cos\left(\frac{2n\pi x}{l} \right) - 1,\ n = 0,1,2,\dots \end{equation}