Answer
There are two local maximum points, with z-coordinates approximately $z=15$ and $z=4.4$. No local minimum points.
Work Step by Step
Graphed with geogebra.
There are two peaks, with z-coordinates approximately $z=15$ and $z=4.4$.
These two points are local maximum points, since there is a region around each in which they have the greatest z-coordinates.
No minimum points.
The "saddle" between the two "hills" is neither a minimum nor a maximum point because there are points in its vicinity with greater/lower z-values.
