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> **Gronwall Lemma.** Let $I := [x\_0,x\_1]$, $x\_1, > x\_0$, $a,b \in \mathbb{R}$ where $b \geqslant 0$, $y \in C(I)$, such that $$y(x) \leqslant a + b\int\_{x\_0}^x y(t) dt$$ holds for all $x \in I$. Then $$y(x) \leqslant a\exp\left( b(x - x\_0)\right)$$ for all $x \in I$.
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Now I am asked to provide a counterexample if $b < 0$. My question is, how do I generally approach such a task? I think, I try some easy functions like $y \equiv 1$ or $y(x) = -x$, but somehow it did not work. Thanks for any hint.