This provides a geometrical interpretation of critical points of a function of three variables in cylindrical coordinates. You can use the hotspot in the "Domain" window to move around the turquoise point in the 4D Color Graph and the slices. The color graph is colored according to the value of the r, θ and z-partials at that point. If the r-partial is non-negative, then a red layer is added at that point; if the θ-partial is also positive, then a blue layer is added, and if the z-partial is also positive, then a yellow layer is added. At a point where a partial is zero, we can observe a transition of color.

A critical point is a point where all three partials are zero, so it's a point where we observe a change of color in every direction. Hence, it must be a point where all eight colors meet.