Draw the graphs of f(x) = cos x - sin (x /2) and its derivative f'(x) on

Question:

Draw the graphs of f(x) = cos x - sin (x /2) and its derivative f'(x) on the interval [0, 9] using the same axes.
(a) Where on this interval is f'(x) > 0?
(b) Where on this interval is f(x) increasing as x increases?
(c) Make a conjecture. Experiment with other intervals and other function to support this conjecture.