JEE Mains · Maths · STD 12 - 6. Application of derivatives
The sum of all the local minimum values of the twice differentiable function \(\mathrm{F}: \mathrm{R} \rightarrow \mathrm{R}\) defined by \(f(x)=x^{3}-3 x^{2}-\frac{3 f^{\prime \prime}(2)}{2} x+f^{\prime \prime}(1)\) is:
- A \(-22\)
- B \(0\)
- C \(-27\)
- D \(5\)
Answer & Solution
Correct Answer
(C) \(-27\)
Step-by-step Solution
Detailed explanation
\(f(x)=x^{3}-3 x^{2}-\frac{3}{2} f^{\prime \prime}(2) x+f^{\prime \prime}(1)\,....(i)\) \(f^{\prime}(x)=3 x^{2}-6 x-\frac{3}{2} f^{\prime \prime}(2)\,....(ii)\) \(f^{\prime \prime}(x)=6 x-6\,....(iii)\) \(f^{\prime \prime}(2)=12-6=6\) and \(f^{\prime \prime}(1)=0\) Use \((ii)\)…
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