JEE Mains · Maths · STD 12 - 6. Application of derivatives
Let \(f(x)\) be a polynomial of degree \(3\) such that \(f(-1)=10, f(1)=-6, f(\mathrm{x})\) has a critical point at \(\mathrm{x}=-1\) and \(f^{\prime}(\mathrm{x})\) has a critical point at \(\mathrm{x}=1\) Then \(f(x)\) has a local minima at \(x=\)
- A \(4\)
- B \(3\)
- C \(6\)
- D \(9\)
Answer & Solution
Correct Answer
(B) \(3\)
Step-by-step Solution
Detailed explanation
\(f^{\prime \prime}(x)=\lambda(x-1)\) \(f^{\prime}(x)=\frac{\lambda x^{2}}{2}-\lambda x+C\) \(\Rightarrow f^{\prime}(-1)=0 \Rightarrow c=\frac{-3 \lambda}{2}\) \(f(x)=\frac{\lambda x^{3}}{6}-\frac{\lambda x^{2}}{2}-\frac{3 \lambda}{2} x+d\)…
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