If `f(x)=sinx-cosx`, the function decreasing in `0 le x le 2pi` is

Options

A. `[(5pi)/(6),(3pi)/(4)]`
B. `[(pi)/(4),(pi)/(2)]`
C. `[(3pi)/(2),(5pi)/(2)]`
D. none of these

Answer

D

Explanation

Given `f(x)=sinx-cosx`
`thereforef'(x)=cosx+sinx`
`=sqrt(2)cos(x-(pi)/(4))`
`becausef(x)` is decreasing
`thereforef'(x)lt0`
`implies(pi)/(2)lt(x-(pi)/(4))lt(3pi)/(2)`
`implies(3pi)/(4) lt x lt (7pi)/(4)`