A function $f$ such that $f(0) > 0$, $f'(0) = 0$, and as $x$ goes to infinity, $f(x)$ approaches $0$?

Question

I have been playing around with many functions without much success. The function should have a single inflection point if possible.

Drawn on a Whiteboard

Answer 1

The first thing that came to my mind is $f(x)=\frac{1}{x^2+1}$ which has derivative $f'(x)=-\frac{2x}{(x^2+1)^2}$ and we have:

$$f(0)=1>0$$ $$f'(0)=0$$ $$\lim_{x \to \infty} f(x)= 0$$