# Where are the critical points of #tan x#?

##### 2 Answers

#### Explanation:

If you write

The points of discontinuity of the function

Those points correspond to a set of vertical asymptotes for the function

graph{tanx [-10, 10, -5, 5]}

In the sense of critical points from calculus, which are points in the domain where the tangent line is either horizontal, doesn't exist, or has infinite (undefined) slope (if it's vertical), the function

#### Explanation:

You can see from the graph already shown in the other answer that the function

Tangent lines to