Final answer:
To determine the interval on which a function is increasing, find where the function's derivative is positive. Match it to the given options. A. (3, infinity) is correct answer.
Step-by-step explanation:
To determine the interval on which a function is increasing, we need to find where the function's derivative is positive. If the derivative is positive on an interval, then the function is increasing on that interval.
We can determine the derivative of the function and set it greater than zero to find the interval. Once we find this interval, we can match it to the given options.
For example, if the derivative is positive on the interval (3, infinity), then the function is increasing on that interval, so the correct answer would be A.
To determine the interval on which the function is increasing, we need to examine the behavior of the function's slope. If we are given a graphical representation, we look for where the function's graph is rising as we move from left to right. This rising action indicates a positive slope, meaning the function is increasing.
An interval written as (a, b) denotes all the numbers between a and b, but not including a or b themselves. If the interval includes infinity, it signifies that the function continues to increase beyond any finite boundary. An increasing interval such as (3, infinity) means that from just right of 3 onwards, the function is going upwards indefinitely.