Question

Let $f\left(x\right)=x^3-6x^2+12x-3$.Then at $x=2,f\left(x\right)$ has

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

Answer 1

Answer: (D)

neither a maximum nor a minimum

$f\left(x\right)=x^3-6x^2+12x-3$
$f^{\prime }\left(x\right)=3x^2-12x+12$
$f^{\prime \prime }\left(x\right)=6x-12\Rightarrow f^{\prime \prime }\left(2\right)=0$
Hence $x=2$ is neither a maxima nor a minima of $f\left(x\right)$.