Question

The total number of extremum point(s) for $f\left(x\right)=x^3+x^2+x+1$ is

Answer 1

Given, $f\left(x\right)=x^3+x^2+x+1$
$\Rightarrow f^{\prime }\left(x\right)=3x^2+2x+1$
$D=4-12=-8<0$
Hence, $f^{\prime }\left(x\right)>0\forall x\in R$
So, There is no critical points for given $f\left(x\right)$
$\Rightarrow$ There is no possible point of local maxima/minima.