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GATE 2016 CE (CE2) – Question 12

Engineering Mathematics · Calculus: Limits, continuity, mean value theorems, maxima and minima, Taylor series · 1 mark · Multiple choice

The optimum value of $f(x)=x^2-4x+2$ is ______.

  1. 2 (maximum)
  2. 2 (minimum)
  3. −2 (maximum)
  4. −2 (minimum)

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Correct answer: (D) −2 (minimum)

Explanation

Complete the square: f(x)=(x−2)²−2. The squared term is nonnegative and becomes zero at x=2, so the minimum value is−2. Equivalently, f-prime=2x−4 and f-double-prime=2>0. Thus **−2 minimum, D**.