Q109 / 160 · AP EAMCET 2021 (24 Aug Shift 2) · Mathematics

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

  • A
    point of maxima
  • B
    point of minima
  • Correct answer
    C
    point of inflection
  • D
    not a critical point

Solution

We have, $\begin{aligned} f(x) & =x^3-6 x^2-12 x-3 \\ f^{\prime}(x) & =3 x^2-12 x-12 \\ f^{\prime \prime}(x) & =6 x-12 \Rightarrow f^{\prime \prime}(2)=12-12=0\end{aligned}$ Here, $f^{\prime \prime}(x)=0$ at $x=2$ $\therefore x=2$ is a point of inflection.

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

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