Example of strictly concave functions?

Question

I'm learning concave/convex functions. Wikipedia article provides us with example functions of concave or convex. However, it does not provide strictly concave function.

Do you have some examples of strictly concave function? It would be very helpful if you give me the reason how strictly concavity property is used in some analysis.

Answer 1

For any strictly convex function $f$, the function $-f$ will be strictly concave.

An example would be $$f(x)=-x^2$$ for $x\in\mathbb R$.