c)
$\displaystyle g(x)$ is increasing from $\displaystyle -6$ at $\displaystyle x=-2$ untill $\displaystyle x=3$ from where it
decreases to $\displaystyle 2.5$ at $\displaystyle x=4$.
Hence the mininmum of $\displaystyle g$ is $\displaystyle -6$ which occures when $\displaystyle x=-2$
RonL