Find the intervals in which `f(x) = sin x - cos x , 0 lt x lt 2pi` , is strictly increasing or strictly decreasing.

Find the intervals in which the function f(x)=2x^(3) + 9x^2 + 12x + 20 is increasing

Evaluate the integrals int(dx)/(sin^2x cos^2x)

Is the function f(x) = 5x - 4 strictly increasing on R ?

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