CUET · MATHS · PYQ PAPER 2025
If \(x=-1\) and \(x=-2\) are the extreme points of \(f(x)=\alpha \log |x|+\beta x^2+x\) then
- A \(\alpha=\frac{-2}{3}, \beta=\frac{1}{6}\)
- B \(\alpha=\frac{-2}{3}, \beta=-\frac{1}{6}\)
- C \(\alpha=\frac{2}{3}, \beta=\frac{1}{6}\)
- D \(\alpha=\frac{2}{3}, \beta=-\frac{1}{6}\)
Answer & Solution
Correct Answer
(C) \(\alpha=\frac{2}{3}, \beta=\frac{1}{6}\)
Step-by-step Solution
Detailed explanation
\(f'(x) = \frac{\alpha}{x} + 2\beta x + 1\) \(f'(-1)=0 \implies -\alpha - 2\beta + 1 = 0 \implies \alpha + 2\beta = 1\) \(f'(-2)=0 \implies -\frac{\alpha}{2} - 4\beta + 1 = 0 \implies \alpha + 8\beta = 2\)…
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