\textbf{116.} The function with the formula $f(x) = \begin{cases} |x^2 - 2x| & ; \quad x < 2 \\ \dfrac{1}{2}x^2 + ax + b & ; \quad x \geq 2 \end{cases}$ is differentiable at $x = 2$. What is $a + b$?
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(1) $2$ \hspace{2cm} (2) $3$ \hspace{2cm} (3) $4$ \hspace{2cm} (4) $5$
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