question_answer 19)

Show that f(x) = sin x is (a)   strictly increasing in (b)   strictly decreasing in (c)   neither increasing nor decreasing in (0, )  

Answer:

f(x) = sin x       f?(x) = cos x (a)   Where       is + ve in Ist quadrant]       is strictly increasing in (b)   When  in 2nd quadrant]              is strictly decreasing in (c)   When  then f?(x) may be > 0 or < 0 is neither increasing nor decreasing in (0, )