Final answer:
The function f(x) = x² + 10 has a positive average rate of change over any interval starting from x > 0 and moving to the right, since the function's values are increasing as x increases.
Step-by-step explanation:
The question asks over which interval the function f(x) = x² + 10 has a positive average rate of change. Considering the function is a parabola opening upwards (since the coefficient of x² is positive), the average rate of change will be positive for intervals where x is increasing. More specifically, since the vertex of this parabola is at x = 0, any interval starting from x > 0 and moving to the right will show a positive average rate of change because the function's values are increasing as x increases.
For example, let's choose the interval from x = 1 to x = 2. We calculate the average rate of change as the change in f(x) values divided by the change in x values, which is [f(2) - f(1)]/[2 - 1] = [(2² + 10) - (1² + 10)]/1 = (14 - 11)/1 = 3/1 = 3, indicating a positive average rate. This would hold true for any interval starting after x = 0 going towards x = ∞.