Question

Is `f(x)=(x-3)(x-2)-x^2` concave or convex at `x=3`?

Answer 1

`f` is a linear function. It is neither concave nor convex.

Explanation:

Simplify to see that `f(x) = -5x+6`.

If more is needed, observe that `f'(x) = -5` and `f''(x) = 0`, so `f` is neither concave nor convex.