Q94 / 180 · KCET 2024 · Mathematics

For the function $f(x)=x^3-6 x^2+12 x-3$ $x=2$ is

  • A
    A point of minium
  • Correct answer
    B
    A point of inflexion
  • C
    Not a critical point
  • D
    A point of maximum

Solution

$\because f(x)=x^3-6 x^2+12 x-3$ $\Rightarrow f^{\prime}(x)=3 x^2-12 x+12$ $\Rightarrow f^{\prime \prime}(x)=6 x-12=6(x-2)$ $\Rightarrow f^{\prime \prime}(2)=0$

Hence, the correct answer is option: 'B'.

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