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If f:R to R given by f(x)=x^(3)+px^(2)+...

If `f:R to R ` given by `f(x)=x^(3)+px^(2)+qx+r,` is then find the condition for which `f(x)` is one-one.

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The correct Answer is:
`p^(2) le 3q`
We have `f(x)=x^(3)+px^(2)+qx+r`
` :. f'(x)=3x^(2)+2px+q, AA x in R`
`implies " Discriminant, " D le 0 " " ` (as coefficient of `x^(2)` is positive)
`implies 4p^(2)-12q le 0`
`implies p^(2) le 3q`
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