Candidates for relative maxima and minima occur where $f^\prime(x) = 0$ and $f ^\prime(x) = \text{DNE}$.
Candidates for points of inflection occur where $f^{\prime\prime}(x) = 0$ and $f^{\prime\prime}(x) = \text{DNE}$.
But these are just CANDIDATES.
You have to conduct other tests before identifying each candidate as the location of a maximum, minimum, or POI.

Once you determine the $x$-value of each relative max, relative min, and POI, recall that maxima and minima are defined as $y$-values.
Use the function $f(x)$ to determine the corresponding $y$-coordinates.