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JEE Main 2024 Mathematics question

MathematicsApplication of DerivativesJEE Main 2024

Let f : R → R be a thrice differentiable function such that f(0) = 0, f(1) = 1, f(2) = –1, f(3) = 2 and f(4) = –2. Then, the minimum number of zeros of (3f′f″ + ff‴)(x) is …..

Answer: 5

Solution

3f′f″ + ff‴ = (f f′)″ = ½(f²)‴. f² has at least 4 zeros (at 0 and one in each of (1, 2), (2,

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Question ID VK-011390