Given the function g(x) = x2 – 10x + 19, determine the average rate of change of the function over the interval 3 < x < 6.

The average rate of change for g(x) on the interval 3 ≤ x ≤ 6 is -1.

Step-by-step explanation:

We want to find the average rate of change of the function:

Over the interval:

The average rate of change is essentially the average slope of the function. So, we want to find the slope between g(3) and g(6).

Evaluate both points:

Thus, we obtain the two points (3, -2) and (6, -5).

The slope between them is:

Therefore, the average rate of change for g(x) on the interval 3 ≤ x ≤ 6 is -1.