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

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

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 (a) increasing in (0,(pi)/(2)) (b) decreasing in ((pi)/(2) ,pi) (c) neither increasing nor decreasing in (0, pi )

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

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) .

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

Prove that the function given by f(x) = x^(3) – 3x^(2) + 3x – 100 is increasing in R.

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