Prove that f(x) = x - sin x is an increasing function.

A function g(x) is defined as g(x) = (1)/(4) f(2x^(2) - 1) + (1)/(2) f(1- x^(2)) and f'(x) is an increasing function. Then g(x) is increasing in the interval

The functions f(x) = tan ^(-1) (sin x +cos x ) , x gt 0 is always an increasing functions on the interval :

Show that the function defined by f(x)=sin (x^2) is a continuous function.

The function f(x) = (x (x - 2))^(2) is increasing in the interval

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

If f(x) = x^(3) + bx^(2) + cx + d and 0 lt b^(2) lt c , then in (-oo, oo) , a)f(x) is a strictly increasing function b)f(x) has local maxima c)f(x) is a strictly decreasing function d)f(x) is bounded

Show that the function given by f(x)=sin x is a) strictly increasing in (0, pi/2) b) Strictly decreasing in (pi/2, pi) c) Neither increasing nor decreasing in (0,pi) .