GATE 2021 BM – Question 31

Engineering Mathematics · Calculus · 1 mark · Numerical answer

Find the minimum of $f(x_1,x_2,x_3)=\tfrac12(x_1^2+x_2^2+x_3^2)-2(x_1+x_2+x_3)$, rounded to the nearest integer.

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Correct answer: -6 to -6

Explanation

Complete the square in each coordinate: f=½[(x₁−2)²+(x₂−2)²+(x₃−2)²]−6. Each squared term is nonnegative and all vanish at x₁=x₂=x₃=2. The global minimum is therefore −6.

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