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JEE Mains · Maths · STD 12 - 6. Application of derivatives

દ્રીતીય વિકલનીય વિધેય  \(\mathrm{F}: \mathrm{R} \rightarrow \mathrm{R}\) કે જે  \(f(x)=x^{3}-3 x^{2}-\frac{3 f^{\prime \prime}(2)}{2} x+f^{\prime \prime}(1)\) દ્વારા વ્યાખ્યાયિત છે તેના બધાજ સ્થાનીય ન્યૂનતમ કિમંતોનો સરવાળો મેળવો.

  1. A \(-22\)
  2. B \(0\)
  3. C \(-27\)
  4. D \(5\)
Verified Solution

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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