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 $x \in[-2,2]?$
1. $f(x)\leq \frac{1}{2} \mid x+1 \mid$
2. $f(x)\leq 2 \mid x+1 \mid$
3. $f(x)\leq \frac{1}{2} \mid x \mid$
4. $f(x)\leq 2 \mid x \mid$