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Show that the function f(x) = (x^3 - 6x^...

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

Text Solution

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`f(x) = (x^(3) - 6x^(2) + 12x - 18)`
`rArr f'(x) = 3x^(2) - 12x + 12`
`= 3 (x^(2) - 4x + 4) = 3(x - 2)^(2) ge 0` for all `x inR`
Thus, `f'(x) ge 0` for all `x in R`
Hence , f(x) is an increasing function on R
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