GATE 2024 MA – Question 26

f:ℝ⁴→ℝ is differentiable and homogeneous of degree 3, with f(p)=6 at p=(1,1/2,1/3,1/4). Find 12f_x₁(p)+6f_x₂(p)+4f_x₃(p)+3f_x₄(p) (integer).

Show answer and explanation

Correct answer: 216 to 216

Explanation

Euler’s identity gives p·∇f(p)=3f(p)=18. The required coefficients are exactly 12 times the coordinates of p, so the expression is 12×18=**216**.

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