JEE Main 2024 Mathematics question
Let the set of all positive values of λ, for which the point of local minimum of the function (1 + x(λ² − x²)) satisfies , be (α, β). Then α² + β² is equal to .......
Answer: 39
Solution
Since x² + x + 2 > 0 always, the inequality needs (x + 2)(x + 3) < 0, so x ∈ (−3, −2). For f(x) = 1 + x(λ² − x²), f′(x) = λ² − 3x² = 0
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