Final answer:
The function f(x) is increasing on intervals [nπ/2, (n+1)π/2) where n is an even integer, because its derivative f'(x) = sin(2x) is positive for these intervals.
Step-by-step explanation:
To determine on what interval the function f(x) is increasing, we must look at its derivative, f'(x) = sin(2x). We know that a function is increasing on intervals where its derivative is positive. The sine function oscillates between +1 and -1 with a period of π radians, so sin(2x) will oscillate with a period of π/2 radians.
Since sin(2x) is positive for the first half of each periodic cycle, f(x) will be increasing where 2x is between 0 and π (or 0 ≤ x ≤ π/2). This pattern repeats every π/2 radians. Therefore, the function f(x) is increasing on intervals [nπ/2, (n+1)π/2) where n is an even integer.