Show that f(x) `=(x^(3) -6x^(2)+12x-8)` does not have any point of local maxima or minima . Hence draw graph

Explanation

`f(x) =x^(3) =6x^(2) +12x -8`
`f(x) =3(x^(2)-4x+4)`
`f(x) =3(x -2)^(2)`
`f(x)=0 " "rArr" " x=2`
But clearly f(x) does not change sigh about x=2. f(2)` lt 0 " and " f(2) lt 0.`So f(x) has no point of maxima or minima . In fact f(x) is a monotonically increasing function for `x in R`