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GATE 2020 ST – Question 13

Calculus · Multivariable Calculus · 1 mark · Multiple choice

On S={(x,y):x²−y²=4}, let f(x,y)=6x+y². Which statement is true?

  1. f is bounded on S.
  2. Its maximum on S is13.
  3. Its minimum on S is−14.
  4. Its minimum on S is−13.

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Correct answer: (D) Its minimum on S is−13.

Explanation

Use y²=x²−4, giving f=x²+6x−4=(x+3)²−13. The constrained x domain is |x|≥2 and includes x=−3, with y=±√5. Thus the minimum−13 is attained, D. Values grow without bound as |x| grows, so there is no finite maximum.

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