Suppose I have a function $f:[a, b]\rightarrow\mathbb{R},~a,b\in \mathbb{R}\cup\{-\infty,\infty\}$. Is there any Computer\Algebra or Symbolic Computing algorithm to determine if $f$ is nonnegative?
For starters, lets suppose $f$ is integrable, continuous and differentiable.
If the answer is negative, what about particular cases of the problem (Rationals, Integer, limited or finite image)?
One possible test is given by $$ \int_{a}^{b}\left[\mathrm{f}\left(\, x\,\right) - \left\vert\mathrm{f}\left(\, x\,\right)\right\vert\right]dx = 0 $$