GATE 2025 PI – Question 44

Engineering Mathematics · Calculus · 2 marks · Numerical answer

Find the rate of change of $f=x^2+2y^2+z$ at (1,1,1) in the direction $3\mathbf i+4\mathbf k$ (integer).

Show answer and explanation

Correct answer: 2 to 2

Explanation

The gradient at the point is (2,4,1). Normalize the direction to (3/5,0,4/5). Their dot product is $2(3/5)+4(0)+1(4/5)=\mathbf2$.

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