Monotonic

A function is monotonic if it never experiences a change from increasing to decreasing, or vice versa.

It is okay for a monotonic function to have a point where it is neither increasing nor decreasing as long as after that it goes back to doing what it was doing before. A horizontal line is monotonic even though it never increases or decreases.

Appendix C

We found this statement:

“The function always has a positive slope on the interval (-∞, ∞) so it is a nondecreasing monotonic function.”

That it is always nondecreasing–yes. But it’s slope is not always positive.

In the moment that x equals 0 it has a slope of zero; in that moment it does not have a positive slope.