GATE AG 2022 • Q16 MCQ • 1 Mark

Section 1: Engineering Mathematics

Calculus

Subtopic: Maxima and minima of function with several independent variables

Question Statement:

The function (x − 2)²(x + 2)² has

Options:

  • (A) minima at +2 and maxima at -2
  • (B) minima at -2 and maxima at +2
  • (C) minima at -2 and +2
  • (D) maxima at -2 and +2

Official Answer Key:

C

Step-by-Step Solution & Explanation

• f(x) = (x²−4)²; f'(x) = 4x(x−2)(x+2); critical points x=0,2,−2. • f(0)=16, f(2)=0, f(−2)=0; since f(x)≥0 always, f(2)=f(−2)=0 are minima, f(0)=16 is a local maximum.

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