5. \( f(x) = \begin{cases}
1 - 2x, & \text{if } x \leq 1 \\
-x^2, & \text{if } x > 1
\end{cases} \)
Let \( f \) be the function given above. Which of the following must be true?
I. \(\lim\limits_{{x \to 1}} f(x)\) exists.
II. \( f \) is continuous at \( x = 1 \).
III. \( f \) is differentiable at \( x = 1 \).
