JEE Main 2024 Mathematics question
Let S = (−1, ∞) and f : S → ℝ be define as . Let p = sum of squares of the values of x, where f(x) attains local maxima on S and q = sum of the values of x, where f(x) attains local minima on S. Then, the value of p² + 2q is .
Answer: 27
Solution
f′(x) = (eˣ − 1)¹¹(2x − 1)⁵(x − 2)⁷(x − 3)¹²(2x − 10)⁶¹, which vanishes at x = 0, 1/2, 2, 3, 5. The factor (x − 3)¹² does not change sign, so x = 3 is not an extremum. The sign of
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