Let f: \mathbb{R} rarr \mathbb{R} be a t...

Let `f: \mathbb{R} rarr \mathbb{R}` be a twice differentiable function such that `f(x+pi)=f(x)` and `f''(x) + f(x) geq 0` for all `x in \mathbb{R}`. Show that `f(x) geq 0` for all `x in \mathbb{R}`.

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