JEE Mains · Maths · STD 12 - 6. Application of derivatives
Let \(\mathrm{f}(\mathrm{x})\) be a cubic polynomial with \(\mathrm{f}(1)=-10\) \(\mathrm{f}(-1)=6\), and has a local minima at \(\mathrm{x}=1\), and \(f^{\prime}(x)\) has a local minima at \(x=-1\). Then \(f(3)\) is equal to .... .
- A \(64\)
- B \(11\)
- C \(22\)
- D \(33\)
Answer & Solution
Correct Answer
(C) \(22\)
Step-by-step Solution
Detailed explanation
\(F^{\prime}(x)=a(x-1)(x+3)\) \(F^{\prime \prime}(x)=6 a(x+1)\) \(F^{\prime}(x)=3 a(x+1)^{2}+b\) \(F^{\prime}(1)=0 \Rightarrow b=-12 a\) \(F(x)=a(x+1)^{3}-12 a x+c\) \(=(x+1)^{3}-12 x-6\) \(F(3)=64-36-6=22\)
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