For every twice differentiable function f: R [-2,2] with (f(0))^2+(f'(0))^2=85, which of the following statement(s) is (are) TRUE?

JEE Advanced 2018 Mathematics question

Mathematics Application of Derivatives JEE Advanced 2018

For every twice differentiable function with , which of the following statement(s) is (are) TRUE?

(A)There exist , where , such that is one-one on the open interval Correct
(B)There exists such that Correct
(C)
(D)There exists such that and Correct

Answer: (A),(B),(D)

Solution

Since , , so . (A) is continuous and non-zero near 0, so is strictly monotonic (one-one) on some interval around 0: true. (B) By the mean value theorem on : : true. (C) Nothing forces this limit; e.g. a bounded

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Question ID VK-026739