KCET · Maths · Application of Derivatives
For the function \(f(x)=x^3-6 x^2+12 x-3\) \(x=2\) is
- A A point of minium
- B A point of inflexion
- C Not a critical point
- D A point of maximum
Answer & Solution
Correct Answer
(B) A point of inflexion
Step-by-step Solution
Detailed explanation
\(\because f(x)=x^3-6 x^2+12 x-3\)
\(\Rightarrow f^{\prime}(x)=3 x^2-12 x+12\)
\(\Rightarrow f^{\prime \prime}(x)=6 x-12=6(x-2)\)
\(\Rightarrow f^{\prime \prime}(2)=0\)
\(\Rightarrow f^{\prime}(x)=3 x^2-12 x+12\)
\(\Rightarrow f^{\prime \prime}(x)=6 x-12=6(x-2)\)
\(\Rightarrow f^{\prime \prime}(2)=0\)
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