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Prove that the function f(x)=x^3-6x^2+12...

Prove that the function `f(x)=x^3-6x^2+12 x-18` is increasing on `R` .

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We have given
`f(x)=x^3-6x^2+12 x-18`
Then we have to prove `f(x)` is increasing on R.
`f(x)=x^3-6x^2+12 x-18`
`f′(x)=3x^2-12x+12`
`f′(x)=3(x^2-4x+4)`
`f′(x)=3(x-2)^2`
`implies f′(x) >=0` for all `x in R`
...
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