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Test whether the following functions are...

Test whether the following functions are increasing or decreasing :
`f(x)=x^(3)-6x^(2)+12x-16, x in R`

Text Solution

Verified by Experts

`f(x)=x^(3)-6x^(2)+12x-16`
`:.f'(x)=("d")/("dx")(x^(3)-6x^(2)+12x-16)`
`=3x^(2)-6xx2x+12xx1-0`
`=3x^(2)-12x+12`
`=3(x^(2)-4x+4)=3(x-2)^(2)gt 0" for all "x in R, x ne 2`
`:.f'(x)gt 0" for all "x in R-{2}`
`:.` f is increasing for all `x in R-{2}`.
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