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Prove that the function f given by f(x)=...

Prove that the function `f` given by `f(x)=x^3-3x^2+4x` is strictly increasing on `R` .

Text Solution

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`F'(x)=(df(x))/dx>0`
`F'(x)=(f(x_2)-f(x_1))/(x2-x1)>0`
`F'(x)>0`
`(df(x))/(dx)=(d(x^3-3x^2+4x))/dx`
`=3x^2-6x+4`
`=3(x^2-2x+1)+1`
`=3(x-1)^2+1`
`3(+ve)+1>0`
...
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