GATE 2021 PI – Question 35

Engineering Mathematics · Calculus · 1 mark · Numerical answer

Find the minimum of $f(x,y,z)=x^2+5y^2+5z^2-4x+40y-40z+300$ (integer).

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Correct answer: 136 to 136

Explanation

Complete squares: $f=(x-2)^2+5(y+4)^2+5(z-4)^2+136$. All squared terms are nonnegative and vanish together at (2,−4,4), giving global minimum **136**.

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