If a function $\"\"$ has a positive average rate of change on the interval $\"\"$ .

Formula for the average rate of change from $\"\"$ to $\"\"$ is $\"\"$ .

Slope of a line could be interpreted as the average rate of change.

Consider the two functions that have positive average rate of change on the interval $\"\"$ .

Graph of $\"\"$ : Graph of $\"\"$ :

$\"\"$ $\"\"$

Observe the above two graphs:

The two example graphs satisfy $\"\"$ , but the function $\"\"$ is not increasing on $\"\"$ .

And the function $\"\"$ in increasing on $\"\"$ .

Therefore, the function $\"\"$ has a positive average rate of change on the interval $\"\"$ , is not necessary increasing on $\"\"$ .

Not necessarily. It just means $\"\"$ .