Question

$f\left(x\right)=x^3-3x^2+6x+7$ has

• A. a minimum only
• B. neither maximum nor minimum
• C. a maximum only
• D. a maximum and a minimum

Answer 1

The correct option is B neither maximum nor minimum

$f\left(x\right)=x^3-3x^2+6x+7$
$\Rightarrow f^{\prime }\left(x\right)=3x^2-6x+6$
$D=6^2-4\left(3\right)\left(6\right)=-36<0$
So,$f^{\prime }\left(x\right)$ will be always positive $\Rightarrow f\left(x\right)$ will be an increasing function.
Hence, $f\left(x\right)$ has neither maximum nor minimum.