Question

The function `f(x)=sqrt(3)sin x-cos x` will increase monotically in the interval(s)
A. `0le x le (pi)/(2)`
B. `-(pi)/(3)le x le (2pi)/(3)`
C. `(5pi)/(3)le x le(8pi)/(3)`
D. `0 le x le pi`

Answer 1

Correct Answer - B::C
`f(x)=2((sqrt(3))/(2)sin x-(1)/(2)cos x)=2 sin (x-(pi)/(6))`
`rArr f(x)` will increase monotically if `-(pi)/(2)le x -(pi)/(6)le(pi)/(2)` and `(3pi)/(2) le x -(pi)/(6)le(5pi)/(2)`
`rArr -(pi)/(3)le x le (2pi)/(3)` nd `(5pi)/(3)le x le (8pi)/(3)`