Which Function Is Monotonic?

A monotonic function is a function which is either entirely nonincreasing or nondecreasing. A function is monotonic if its first derivative (which need not be continuous) does not change sign.

How do you know if a function is monotonic?

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].

Are the functions strictly monotonic?

Also, a function can be said to be strictly monotonic on a range of values, and thus have an inverse on that range of value. For example, if y = g(x) is strictly monotonic on the range [a,b], then it has an inverse x = h(y) on the range [g(a), g(b)], but we cannot say the entire range of the function has an inverse.