Let f(x) = cases |x| & for 0 < |x| 2 1 & for x = 0. cases Then at x = 0, f has

JEE Advanced Mathematics question

Let

f(x) =

Then at , has

Answer: (A)

, while for , . So exceeds all nearby values: a (strict) local maximum at — even though

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Question ID VK-110516