Prove that the function `f` given by `f(x)=logcosx` is strictly increasing on `(-pi//2,\ 0)` and strictly decreasing on `(0,\ pi//2)` .

Show that the function given by f(x)=e^(2x) is strictly increasing on R.

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

Prove that the function f(x)=cosx is strictly increasing in (pi,\ 2pi)

Prove that function given by f(x)=sin x is (i) Strictly increasing in (-(pi)/(2),(pi)/(2)) (ii) Strictly decreasing in ((pi)/(2),(3pi)/(2))

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

Show that the function f given by f(x)=x^3-3x^2+4x ,x in R is strictly increasing on R.

Prove that the function f(x)=cosx is strictly decreasing in (0,\ pi)

Prove that the function f(x)=tanx-4x is strictly decreasing on (-pi//3,\ pi//3) .

Prove that the function f(x)=tanx-4x is strictly decreasing on (-pi//3,\ pi//3) .

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