Let f: R → R be a differentiable function such that f(0)=2. If |(d f)/(d x)| ≤ 3, for all x ∈ R, then f(1) lies in the interval

Let $\displaystyle f: \mathbb{R} \rightarrow \mathbb{R}$ be a differentiable function such that $\displaystyle f(0)=2$. If $\displaystyle \left|\frac{d f}{d x}\right| \leq 3$, for all $\displaystyle x \in \mathbb{R}$, then $\displaystyle f(1)$ lies in the interval