If f(x)=x^3+b x^2+c x+d and 0<b^2<c , th...

If `f(x)=x^3+b x^2+c x+d` and `0

f(x) is strictly increasing function

f(x) has local maxima

f(x) is a strictly decreasing function

f(x) is bounded

Text Solution

Verified by Experts

The correct Answer is:

`f(x) =x^(3)+bx^(2)+cx+d,0ltb^(2)ltc`
`f(x) =3x^(2)+2bx+c`
Discriminant =`4b^(2)-12c=4(b^(2)-3c)ltc`
`therefore f(X) gt 0 forall x in R`
Thus f(X) is strictly increasing `forall x inR`

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