f(x) = cos x is neither increasing nor decreasing in `(0,2pi)`

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

Prove that the function / defined by f(x) = x^(2) -x+1 is neither increasing nor decreasing in (-1, 1). Hence, find the intervals in which f(x) is: (i) strictly increasing , (ii) strictly decreasing.

Show that the function x^2 - x+1 is neither increasing nor decreasing on (0,1).

Prove that the function x^2 + x+1 is neither increasing nor decreasing on (-1,0)

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

f(x) = cos x is strictly increasing in (pi,2pi)

Let f(x)=sin(cosx), then check whether it is increasing or decreasing in [0,pi//2].

Find the value of 'x' for which f(x) = x^x , x > 0 is strictly increasing or decreasing.