jee-advanced 2000 Q28

jee-advanced · India · screening Stationary points and optimisation Composite or piecewise function extremum analysis

28. Let $f ( x ) = \left\{ \begin{array} { c l l } | x | & \text { for } 0 < | x | \leq 2 \\ 1 & \text { for } & x = 0 . \end{array} \right.$
Then at $\mathrm { x } = 0 , \mathrm { f }$ has :
(A) A local maximum
(B) no local maximum
(C) a local minimum
(D) no extremum

28. Let $f ( x ) = \left\{ \begin{array} { c l l } | x | & \text { for } 0 < | x | \leq 2 \\ 1 & \text { for } & x = 0 . \end{array} \right.$

Then at $\mathrm { x } = 0 , \mathrm { f }$ has :\\
(A) A local maximum\\
(B) no local maximum\\
(C) a local minimum\\
(D) no extremum\\

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