The image shows a math problem that asks to calculate the average rate of change for the function $g(x) = 4x^2 - 5x + 1$ over different intervals. There are six given intervals:

1. $2 \leq x \leq 4$
2. $2 \leq x \leq 3$
3. $2 \leq x \leq 2.5$
4. $2 \leq x \leq 2.25$
5. $2 \leq x \leq 2.1$
6. $2 \leq x \leq 2.01$

The average rate of change formula:

The average rate of change of a function $g(x)$ over an interval $[a, b]$ is given by: $\text{Average rate of change} = \frac{g(b) - g(a)}{b - a}$ We will calculate this for each interval provided.

Would you like me to go through these calculations one by one?