Monotonic
From AoPSWiki
A real function or sequence is called monotonic if it either constantly increases or decreases. Thus, the sequence 
of powers of 2 is monotonically increasing because each term is larger than the previous. The function 
is monotonically decreasing on the interval ![(-\infty, 0]](http://alt2.artofproblemsolving.com/Forum/latexrender/pictures/d/9/8/d98c9b9bdb28cb35d043d7e5818fa9be92ea468f.gif)
and monotonically increasing on the interval 
. However, the function is not monotonic over the entire real line because it sometimes increases and sometimes decreases.
More formally, a function 
is monotonically increasing (resp. decreasing) if 
(resp. 
. The function is strictly monotonic if, in addition, 
.
A differentiable function is monotonically increasing (resp. decreasing) if and only if its derivative is nonnegative (resp. nonpositive).
