The length of the largest continuous interval in which the function `f(x)=4x-tan2x` is monotonic is (a) `pi/2` (b) `pi/4` (c) `pi/8` (d) `pi/(16)`

The length of the longest interval in which the function 3sinx-4sin^3x is increasing is pi/3 (b) pi/2 (c) (3pi)/2 (d) pi

An extremum value of the function f(x)=(a r csinx)^3+(a r ccosx)^3 is (7pi^3)/8 (b) (pi^3)/8 (c) (pi^3)/(32) (d) (pi^3)/(16)

For f(x)=sin^2x ,x in (0,pi) point of inflection is: pi/6 (b) (2pi)/4 (c) (3pi)/4 (d) (4pi)/3

The maximum value of the function f(x)=sin(x+pi/6)+cos(x+pi/6) in the interval (0,pi/2) occurs at (a) pi/(12) (b) pi/6 (c) pi/4 (d) pi/3

Range of function f(x)=cot^(-1)(2x-x^2), is (a) [pi/4,(3pi)/2] (b) [0,pi/4] [0,pi/2] (d) [pi/4,pi]

The value of c in Lagranges theorem for the function f(x)=logsinx in the interval [pi/6,(5pi)/6] is (a) pi/4 (b) pi/2 (c) (2pi)/3 (d) none of these

The angle of intersection of the curves y=2\ sin^2x and y=cos2\ x at x=pi/6 is (a) pi//4 (b) pi//2 (c) pi//3 (d) pi//6

The largest interval lying in (-pi/2,pi/2) for which the function [f(x)=4^-x^2+cos^(-1)(x/2-1)+log(cosx)] is defined, is (1) [0,pi] (2) (-pi/2,pi/2) (3) [-pi/4,pi/2) (4) [0,pi/2)

The largest interval lying in (-pi/2,pi/2) for which the function [f(x)=4^-x^2+cos^(-1)(x/2-1)+log(cosx)] is defined, is (1) [0,pi] (2) (-pi/2,pi/2) (3) [-pi/4,pi/2) (4) [0,pi/2)

Show that the function f(x)=sin(2x+pi//4) is decreasing on (3pi//8,\ 5pi//8) .