Statement 1: Let `f(x)=sin(cos x)in[0,pi/2]dot` Then `f(x)` is decreasing in `[0,pi/2]` Statement 2: `cosx` is a decreasing function `AAx in [0,pi/2]`

Let f be the function f(x)=cosx-(1-(x^2)/2)dot Then f(x) is an increasing function in (0,oo) f(x) is a decreasing function in (-oo,oo) f(x) is an increasing function in (-oo,oo) f(x) is a decreasing function in (-oo,0)

Statement 1: If f(0)=0,f^(prime)(x)=ln(x+sqrt(1+x^2)), then f(x) is positive for all x in R_0dot Statement 2: f(x) is increasing for x >0 and decreasing for x<0

Which of the following functions are decreasing on 0,(pi)/(2) ?

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 )

if f(x)= sinx + cosx for 0 < x < pi/2

Solve |sinx+cosx|=|sinx|+|cosx|,x in [0,2pi]dot

Prove that f(x)=(sinx)/x is monotonically decreasing in [0,pi/2]dot Hence, prove that (2x)/pi

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

If the function f(x) = 2cotx+(2a+1) ln|cosec x| + (2-a)x is strictly decreasing in (0, pi/2) then range of a is

Find the absolute extreme of the function f(x) = 2 cos x in [0, 2pi]