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

For the function $f(x)=x^3-6 x^2-12 x-3$, $x=2$ is a
  1. point of maxima
  2. point of minima
  3. point of inflection
  4. 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.

Asked in: AP EAMCET 2021 (24 Aug Shift 2)

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