The function f(x) = 2|x| + |x + 2| - ||x + 2| - 2|x| | has a local minimum or a local maximum at x =

JEE Advanced 2013 Mathematics question

The function has a local minimum or a local maximum at x =

(A)−2Correct
(B)Correct
(C)2
(D)

Answer: (A),(B)

Solution

With a = 2|x| and b = |x + 2|, , so . The two graphs meet where 2|x| = |x + 2|, i.e. at and x = 2. For x < −2, f = 2|x + 2|, decreasing to f(−2) = 0; on , f = 2(x + 2), increasing to

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Question ID VK-026227