JEE Main 2024 Mathematics question
Let the set of all values of p, for which f(x) = (p² − 6p + 8)(sin²2x − cos²2x) + 2(2 − p)x + 7 does not have any critical point, be the interval (a, b). Then 16ab is equal to .
Answer: 252
Solution
f(x) = −(p² − 6p + 8)cos 4x + 2(2 − p)x + 7, so f′(x) = 4(p − 2)(p − 4) sin 4x + 2(2 − p). f′ has no zero when sin 4x ≠ 1/(2(p −
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