Question

On what intervals within [0, T) is f increasing? (T is the period of the function. Enter your answer using interval notation. If an answer does not exist, enter DNE.)
y = 2 sin x

Answer 1

Since there is only a factor of two in front, the period of the function is unchanged: T = 2pi. Differentiating we get that y' = 2cos(x), which is positive on [0, pi/2)U(3pi/2, 2pi] and negative on (pi/2, 3pi/2).

Interval of Increase: [0, pi/2)U(3pi/2, 2pi]
Interval of Decrease: (pi/2, 2pi/2)
(Note there are open intervals since at the critical points pi/2 and 3pi/2 the function is neither increasing or decreasing)

Answer 2

thank you)