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If f(x) = {{:(|x|",", "for",,0 lt |x| le...

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

Text Solution

Verified by Experts

The correct Answer is:
A
It is clear from figure that at `x =0, f(x)` is not continuous.
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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