Question

If $f\left(x\right)=k{x}^3-9x^2+9x+3$ is monotonically increasing in R, then

• A. $k<3$
• B. $k\le 2$
• C. $k\ge 3$
• D. $k>2$

Answer 1

The correct option is C $k\ge 3$

$f^{\prime }\left(x\right)=3k{x}^2-18x+9=3[k{x}^2-6x+3]\ge 0,\forall x\in R$
$\Rightarrow D=b^2-4ac\le 0,k>0,i.e,36-12k\le 0$
$\Rightarrow k\ge 3$.