Let 𝑓:ℝ→ℝ be defined as follows: f(π‘₯)=(|π‘₯|/2 βˆ’π‘₯)(π‘₯βˆ’|π‘₯|/2 ) Which of the…

GATE Β· 2026 Β· CS Β· Set 1 Β· Computer Science & IT

Let 𝑓:ℝ→ℝ be defined as follows:

f(π‘₯)=(|π‘₯|/2 βˆ’π‘₯)(π‘₯βˆ’|π‘₯|/2 )

Which of the following statements is/are true?

  1. A.

    f has a local maximum

  2. B.

    f has a local minimum

  3. C.

    fβ€² is continuous over ℝ

  4. D.

    fβ€² is not differentiable over ℝ

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