Final answer:
The average rate of change of f(x) = tan x from 0 to π/6 is (6√3)/π.
Step-by-step explanation:
The average rate of change of a function f(x) from 0 to π/6 can be found by evaluating the difference in function values divided by the difference in x-values over the interval. In this case, the function is f(x) = tan x.
Using the formula for average rate of change, we have:
Average rate of change of f from 0 to π/6 = (f(π/6) - f(0)) / (π/6 - 0) = (tan(π/6) - tan(0)) / (π/6) = (1/√3 - 0)/(π/6) = (6√3)/π