Prove that the function f given by f(x) = log sin x is increasing on `(0,(pi)/(2))` and decreasing on `((pi)/(2),pi)` .

Prove that the function f given by f (x) = log |cos x| is decreasing on (0,(pi)/(2)) and increasing on ((3pi)/(2) ,2pi) .

Show that the function given by f (x) = sin x is (a) increasing in (0,(pi)/(2)) (b) decreasing in ((pi)/(2) ,pi) (c) neither increasing nor decreasing in (0, pi )

Prove that the function given by f(x) = cos x is (a) strictly decreasing in (0, pi) .

Show that the function given by f(x) = sin x is (a) strictly increasing in (0, (pi)/2) .

Prove that the function given by f(x) = cos x is (b) strictly increasing in (pi,2 pi) .

Show that the function given by f(x) = sin x is (b) strictly decreasing in ((pi)/2, pi) .

Prove that the function given by f(x) = cos x is (c) neither increasing nor decreasing in (0 , 2pi) .

Show that the function given by f(x) = sin x is (c) neither increasing nor decreasing in (0 , pi) .

Prove that the function f given by f(x) = x^(2) - x + 1 is neither increasing nor decreasing strictly on (-1,1).

Find the intervals in which the function f given by f(x) = 2x^(2) – 3x is (a) increasing (b) decreasing