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If `f(x) = {{:(|x|",", "for",,0 lt |x| le 2), (1",", "for,, x =0):}`. Then, at x = 0, ` f ` has

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If `f(x) = {{:(|x|",", "for",,0 lt |x| le 2), (1",", "for,, x =0):}`. Then, at x = 0, ` f ` has
A. a local maximum
B. no local maximum
C. a local minimum `
D. no extremum
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Correct Answer - A
It is clear from figure that at `x =0, f(x)` is not continuous. image
Here, ` f(0) gt RHL ` at ` x = 0 and f (0) gt LHL` at ` x=0`
So, local maximum at ` x =0`
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