AP EAMCET · Maths · Application of Derivatives
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
- C point of inflection
- D not a critical point
Answer & Solution
Correct Answer
(C) point of inflection
Step-by-step Solution
Detailed explanation
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.
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