`c)` Đúng

`f(x)=sin2x+x`

`-> f'(x)=(sin2x+x)'`

`-> f'(x)=(sin2x)'+x'`

`-> f'(x)=2cos2x+1`

`f'(x)=0`

`-> 2cos2x+1=0`

`-> 2cos2x=-1`

`-> cos2x=-1/2`

`-> cos2x=cos([2pi]/3)`

`-> 2x=[2pi]/3+k2pi(k in ZZ)` hoặc `2x=-[2pi]/3+k2pi(k in ZZ)`

`-> x=[pi]/3+kpi(k in ZZ)` hoặc `x=-[pi]/3+kpi(k in ZZ)`

Ta có:

`x in [0; pi]`

`-> 0<=x<=pi`

Xét `x=[pi]/3+kpi`:

`0<=[pi]/3+kpi<=pi`

`-> -[pi]/3<=kpi<=[2pi]/3`

`-> -1/3<=k<=2/3`

`-> k =0 -> x=[pi]/3`

Xét `x=-[pi]/3+kpi`:

`0<=-[pi]/3+kpi<=pi`

`-> [pi]/3<=kpi<=[4pi]/3`

`-> 1/3<=k<=4/3`

`-> k =1 -> x=[2pi]/3`

`d)` Sai

Khi `x=0` thì `f(0)=sin0+0=0`

Khi `x=pi` thì `f(pi)=sinpi+pi=pi`

Khi `x=[pi]/3` thì `f([pi]/3)=sin([2pi]/3)+[pi]/3=[sqrt3]/2+[pi]/3`

Khi `x=[2pi]/3` thì  `f([2pi]/3)=sin([4pi]/3)+[pi]/3=-[sqrt3]/2+[pi]/3`

`->` GTLN `f(x)=pi`