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Consider a differentiable function $f(x)$ on the set of real numbers, such that $f(-1)=0$ and $ \mid f’(x) \mid \leq 2.$ Given these conditions, which one of the following inequalities is necessarily true for all $x \in[-2,2]?$

- $f(x)\leq \frac{1}{2} \mid x+1 \mid$
- $f(x)\leq 2 \mid x+1 \mid $
- $f(x)\leq \frac{1}{2} \mid x \mid$
- $f(x)\leq 2 \mid x \mid$