Answer
The table in Exercise 13 matches with graph $(d)$.
Work Step by Step
Here we see that $f'(a)$ does not exist but $f'(b)$ exists and equals $0$.
In graphs $(b)$ and $(c)$, both the points at $x=a$ and $x=b$ are local minimum or maximum of the graph; and since the graph at these points are smooth, $f'(a)$ and $f'(b)$ must both exist and equal $0$, according to Theorem 2.
In graph $(a)$, though the sharp point at $x=a$ indicates that $f'(a)$ does not exist, yet the sharp point at $x=b$ also indicates the same thing, which here $f'(b)=0$.
Therefore, only graph $(d)$ correctly portrays the table in Exercise 13.
