Which of the following functions are bounded in the interval as indicated? `f(x)=sin x, x in R`

Find the greatest and the least values of the following functions on the indicated intervals : f(x) =2 " sin x + sin 2 x on" [ 0,3/2pi]

Verify Rolle's theorem for each of the following functions on indicated intervals; f(x)=sin^(2)x on 0<=x<=pi f(x)=sin x+cos x-1 on [0,(pi)/(2)]f(x)=sin x-sin2x on [0,pi]

Show that the following functions are increasing in the indicated intervals f(x) = (x)/(sinx), 0 < x< pi/2

Find the greatest and the least values of the following functions on the indicated intervals : f(x) = x-2lnx on [1,e]

Find the intervals in which the following functions are positive and in which they are negative f(x) = x ( x- 2) ( x - 4)

Show that the following functions are increasing in the indicated intervals f(x) = x^3 - 27 x, x 3

Show that the following functions are increasing in the indicated intervals f(x) = -(x)/(2) + sinx , - pi/3 < x< pi/3

Show that the following functions are increasing in the indicated intervals f(x) = (1)/(1+x^2) , x le 0

Show that the following functions are increasing in the indicated intervals f(x) = 1 - 1/x , x< 0