Moderate# Mean Value Theorem: When It Fails

APCALC-Y@OC1E

A function $g$ is continuous for $-3\le x\le 3$. Additionally, $g(-3)=12$ and $g(3)=24$.

If there exists no value of $c$ over $-3 < c < 3$ for which $g^{ \prime }\left( c \right) =2$, which statement below must be true?