#$14$: $[$No Calculator$]$

Let $g$ be a differentiable function with $g(0)=5.$

The graph of a continuous function $f,$ the derivative of the function $g,$ is shown above on the interval $-2,9.$

$($a$)$ Find $g(-2)$ and $g(4).$ Show the work that leads to your answer. $[4]$

$($b$)$ On what intervals is the function $g$ both increasing and concave up$?$ Justify your answer. $[3]$