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  1. GATE2019-90
  2. GATE2019-90
  3. GATE2019-90
  4. GATE2019-90

Consider a differentiable function $f(x)$ on the set of real numbers, such that $f(-1)=0$ and $|f’(x)| \leq2.$ Given these conditions, which one of the following inequalities is necessarily true for all $x \in[-2,2]?$

  1. $f(x)\leq \frac{1}{2}|x+1|$
  2. $f(x)\leq 2|x+1|$
  3. $f(x)\leq \frac{1}{2}|x|$
  4. $f(x)\leq 2|x|$
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