GATE 2014 EC (EC4) – Question 12
Find the magnitude of the gradient of $f(x,y,z)=x^2+3y^2+z^3$ at (1,1,1).
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Correct answer: 6.8 to 7.2
Explanation
For f=x²+3y²+z³, the gradient is(2x,6y,3z²). At(1,1,1)it becomes(2,6,3), whose Euclidean norm is√(4+36+9)=√49=**7**. The question asks the magnitude, not the gradient vector.