Question

Question #ed9fd

Answer 1

See below.

Explanation:

The following answer using definitions and notations like those in Calculus by James Stewart.

By definition: A function `f` is increasing over an interval `I` if and only if for every `x_1` and `x_2` in `I` with `x_1 < x_2`, `f(x_1) < f(x_2)`.

The interval may be open, closed or half-open.

In many calculus classes and calculus textbooks, questions are phrased to ask students to find the open intervals on which a function is increasing and the open intervals on which it is decreasing.

For example `f(x) = x^2` is increasing on any interval that contains no negative numbers.
So `f` is increasing on `[0,5]`
and on `[2,9)` and so on.

A typical text question would say `f` is increasing on `(0,oo)` because they are giving the maximal open interval on which the function is increasing.

Other notation

For the open interval I have denoted `(0,oo)` some will use `]0,oo[`.