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GATE 2018 EE – Question 22

Engineering Mathematics · Calculus: Directional derivatives · 1 mark · Multiple choice

The value of the directional derivative of the function $\Phi(x,y,z)=xy^2+yz^2+zx^2$ at the point $(2,-1,1)$ in the direction of the vector $\mathbf p=\mathbf i+2\mathbf j+2\mathbf k$ is

  1. 1
  2. 0.95
  3. 0.93
  4. 0.9

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Correct answer: (A) 1

Explanation

$\nabla\Phi=(y^2+2zx,\ 2xy+z^2,\ 2yz+x^2)$, which at $(2,-1,1)$ is $(5,-3,2)$. The unit vector is $\frac{(1,2,2)}{3}$, so the derivative is $\frac{5-6+4}{3}=1$.