If `f(x)=x^3+b x^2+c x+d` and `0 le b^2 le c ,` then a)`f(x)` is a strictly increasing function b)f(x) has local maxima c)`f(x)` is a strictly decreasing function d)`f(x)` is bounded

Options

A. f(x) is strictly increasing function
B. f(x) has local maxima
C. f(x) is a strictly decreasing function
D. f(x) is bounded

Answer

1

Explanation

`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`