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The minimum of \(f(x) = |x + 2|, x \in \mathbb{R}\) occurs at

  • A.\(x = 0\)
  • B.\(x = 2\)
  • C.\(x = 1\)
  • D.\(x = -2\)
  • E.\(x = -1\)

Answer: D

The minimum occurs at \(x = -2\).

\(|x + 2| \ge 0\) for all x, with equality only when \(x + 2 = 0\). So the minimum value 0 is attained at \(x = -2\).

At 0, 1, 2 and −1 the function takes the values 2, 3, 4 and 1, all larger than 0.

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