Answer:
If a function is increasing, the average rate of change between any 2 points must be positive.
If we have an increasing function, the average rate of change between any two points must always be positive.
For an increasing function f(x), we have that if:
b > a
Then:
f(b) > f(a).
Now, we define the average rate of change on an interval (a, b) as:
[tex]R = \frac{f(b) - f(a)}{b - a}[/tex]
In this case, because:
b > a
f(b) > f(a)
Then:
b - a > 0
f(b) - f(a) > 0.
So both numerator and denominator are positive, which implies that the quotient must be positive.
Then, if we have an increasing function, the average rate of change between any two points must always be positive.
If you want to learn more about average rate of change, you can read:
https://brainly.com/question/8728504
