GATE AG 2016 • Q4 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Matrices and determinants

Question Statement:

The function f(x) = x² − x − 6 is

Options:

  • (A) minimum at x = ½
  • (B) maximum at x = ½
  • (C) minimum at x = −½
  • (D) maximum at x = −½

Official Answer Key:

A

Step-by-Step Solution & Explanation

f'(x) = 2x − 1. Setting f'(x)=0 gives x = ½. f''(x) = 2 > 0 for all x, so the critical point is a minimum, located at x = ½ → option (A). Options (C)/(D) use the wrong sign of the stationary point; (B) has the right point but wrong nature.

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