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JEE Mains · Maths · STD 12 - 6. Application of derivatives
If \( x=-1 \) and \( x=2 \) are extreme point of \(f\left( x \right) = \alpha \log \left| x \right| + \beta {x^2} + x\) then \(\left( {\alpha ,\beta } \right)\)
- A \(\left( {2, - \frac{1}{2}} \right)\)
- B \(\left( {2,\frac{1}{2}} \right)\)
- C \(\left( { - 6,\frac{1}{2}} \right)\)
- D \(\left( { - 6, - \frac{1}{2}} \right)\)
Answer & Solution
Correct Answer
(A) \(\left( {2, - \frac{1}{2}} \right)\)
Step-by-step Solution
Detailed explanation
\(f'\left( x \right) = \frac{\alpha }{x} + 2\beta x + 1\) at \(x = - 1,2 \Rightarrow f'\left( x \right) = 0\) \( \Rightarrow \,\,\,\, - \alpha - 2\beta + 1 = 0\,\,\,....\left( 1 \right)\) \(\frac{\alpha }{2} + 4\beta + 1 = 0\,\,\,\,....\left( 2 \right)\)…
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