Question

The function $f\left(x\right)=x^3+a{x}^2+bx+c,a^2\le 3b$ has

• A. one maximum value
• B. one minimum value
• C. no extreme value
• D. one maximum and one minimum value

Answer 1

The correct option is C

no extreme value

$f^{\prime }\left(x\right)=3x^2+2ax+bD=4(a^2-3b)\le 0\forall x\in R\Rightarrow f^{\prime }\left(x\right)\ge 0\forall x\in R\therefore f\left(x\right)\text{is increasing on R}$