Answer
Yes.
Work Step by Step
General formula for average rate of change from a to b: $\frac{f(b)-f(a)}{b-a}.$
We know that $b\gt a$ and $\frac{f(b)-f(a)}{b-a}\gt0$. Hence the numerator must be positive too, thus$f(b)\gt f(a)$, therefore it is increasing.
