Function

f(z) = z in cylindrical coordinates

Domain

z is an element of the set of all Real numbers

Graphs

Derivative

With respect to z: 1

With this derivative, there is no value that will make 1 = 0, therefore there are no critical points. The graph shows that there is not a minimum or maximum since the graph will continue to grow to positive and negative infinity.

Integral

With respect to z: ( ¹/₂ ) z²

Interesting Features

When working with this function, there are many different items to look at. The first item is that the plot is done in cylindrical coordinates. The radius of the circle plotted is the same as the height. This causes the growing cone as shown in the graph.