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)`

Options

A. `pi//2`
B. `pi//4`
C. `pi//8`
D. `pi//16`

Answer

2

Explanation

`(X) =4-2 sec ^(2) 2x=2(1-tan^(2) 2x)`
for the continous domain `-((pi)/(4),(pi)/(4)),f(x)ge0 in [(-pi)/(8),(pi)/(8)] "and" f(x)le0 in (-(pi)/(4),(pi)/(8))]cup[(pi)/(8),(pi)/(4)`
So the required largest continous interval is `[(-pi)/(8),(pi)/(8)]` and length is `(pi)/(4)`