Find the intervals of monotonicity of the following functions.
`(i) f(x) =-x^(3) +6x^(2)-gx-2`
`(ii) f(x) =x+(1)/(x+1)`
(iii) `f(x) =x. e^(x-x^(2))`
(iv) `f(x) =x- cosx`

Answer

(i) `I in [1,3] ; D in (-oo, 1] uu(3,oo)`
(ii) `I in (-oo ,-2) uu [0,oo);D in [ -2,-1)uu(-1,0]`
(iii) ` I in [-(1)/(2),1] ; D in (-oo, -(1)/(2)] uu [1,oo)`
(iv) I for ` x in R`