Question

Is `f(x)=tanx` concave or convex at `x=0`?

Answer 1

It is neither.

Explanation:

`f''(x) = 2sec^2xtanx` which is negative for `x < 0` and positive for `x > 0`.

The concavity of the graph changes at `x=0`, so `(0,0)` is an inflection point..