JEE Main 2024 Mathematics question
If , ∀ x ≠ 0 and y = 9x²f(x), then y is strictly increasing in:
Answer: (D)
Solution
9f(x) = 5x² − 4/x² − 2, so y = 5x⁴ − 2x² − 4 and y′ = 4x(5x² − 1) > 0 for −1/√5 < x < 0 and x > 1/√5.
If , ∀ x ≠ 0 and y = 9x²f(x), then y is strictly increasing in:
9f(x) = 5x² − 4/x² − 2, so y = 5x⁴ − 2x² − 4 and y′ = 4x(5x² − 1) > 0 for −1/√5 < x < 0 and x > 1/√5.