Let f:(0, ) R be a twice differentiable function such that _ t x f(x) t-f(t) x t-x = ^2x for all x (0, ). If f ( 6 )=- 12 , then which of the following statement(s) is (are) TRUE?

JEE Advanced 2018 Mathematics question

Let be a twice differentiable function such that

=x\ for all x(0,π).

If , then which of the following statement(s) is (are) TRUE?

Answer: (B),(C),(D)

By L'Hospital's rule (differentiate with respect to ), the limit is , i.e. . So ; gives , hence . (A)

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Question ID VK-026795