Answer
Since the Second Derivative Test is inconclusive, the First Derivative Test should be used in this case.
Work Step by Step
The First Derivative Test can be used to tell whether or not a critical point is a local maximum or minimum, as follows: If $(c, f(c))$ is a critical point, we investigate the sign of $f'$ or points that are just to the left and just to the right of $c$. If the sign of $f'$ changes from positive to negative, then $f$ is changing from increasing to decreasing at $c$, so there is a local maximum at $c$. If the signs of $f'$ are changing from negative to positive, then $f$ is changing from decreasing to increasing at $c$, so there is a local minimum at $c$. If the signs of $f'$ are the same on either side of $c$, then there is neither kind of local extremum at $x = c$.
