Final answer:
The average rate of change of the function f(x) = 3x over the interval [1, 4] is calculated using the formula f(b) - f(a)}{b - a}, which yields an average rate of change of 3.
Step-by-step explanation:
The average rate of change of a function over an interval is calculated by finding the difference in the function values at the endpoints of the interval and dividing it by the difference in the x-values.
In this case, we have the function f(x) = 3x and the interval [1, 4].
Plugging in the values, the average rate of change is (f(4) - f(1)) / (4 - 1) = (3(4) - 3(1)) / (4 - 1) = (12 - 3) / 3 = 9 / 3 = 3.
Therefore, the correct option is Option 1: 3.