How do you know if monotonic is increasing or decreasing?

Test for monotonic functions states: Suppose a function is continuous on [a, b] and it is differentiable on (a, b). If the derivative is larger than zero for all x in (a, b), then the function is increasing on [a, b]. If the derivative is less than zero for all x in (a, b), then the function is decreasing on [a, b].

What is the difference between strictly increasing and monotonically increasing?

In particular, monotonically increasing is the same as increasing, strictly monotonically increasing the same as strictly increasing. ... That is, a monotonically increasing function is nondecreasing over its domain and is also an increasing function since it is non-decreasing over any subset of the domain.