I need help with this question:
f(x) = sin(2x) + cos(2x) where x is an element of [0,pie].
Find the interval on which this function is increasing and decreasing.
I know that I must calculate f'(x) > 0 and f'(x) < 0
But I'm not good at differentiating trigonometric functions and at finding the intervals.
I would very grateful for any help.
Find where the derivative is zero. You will get a list of x-coordinates. Put them in order from least to greatest. Then the intervals to check are (0,x_1), (x_1,x_2), ..., (x_k,\pi) for however many intervals there are. Plug one value from each interval into the derivative. That will tell you the sign of the derivative on each interval.