Final answer:
The function f(x) = x^2 + 10 has a positive average rate of change for all real values of x.
Step-by-step explanation:
To find the interval over which the function f(x) = x^2 +10 has a positive average rate of change, we need to determine when the function is increasing.
The average rate of change of a function can be represented by the slope of a secant line between two points on the function.
In this case, we can examine the values of x to determine when the function is increasing.
Since the coefficient of x^2 is positive, the function opens upwards and therefore increases for all real values of x.
So, the interval over which f has a positive average rate of change is (-∞, ∞).