A function `f(x)=max[sin x, cosx, 1-cosx}` is NOT derivable for some `x in [0, 2pi]` which may lie in the interval

The function f(x)=sin^(-1)(cosx) is

Consider the following statements : 1. The function f(x)=sinx decreases on the interval (0,pi//2) . 2. The function f(x)=cosx increases on the interval (0,pi//2) . Which of the above statements is/are correct ?

Consider the functions f(x)=sinx and g(x)=cosx in the interval [0,2pi] Find the x coordinates of the meeting points of the functions.

The function f(x) = (1-sin x + cos x)/(1+sin x + cosx) is not defined at x = pi . The value of f(pi) , so that f(x) is continuous at x = pi is

The function f(x) = (1-sin x + cos x)/(1+sin x + cosx) is not defined at x = pi . The value of f(pi) , so that f(x) is continuous at x = pi is

If x in (0,pi//2) , then the function f(x)= x sin x +cosx +cos^(2)x is

If x in (0,pi//2) , then the function f(x)= x sin x +cosx +cos^(2)x is

Verify Rolle's Theorem for the functions : f(x)=sinx+cosx in the interval [0,2pi]