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Let, $f\left ( x,y, z \right ) = 4x^{2} + 7xy + 3xz^{2}$. The direction in which the function $\text{f(x, y, z)}$ increases most rapidly at point $P = (1,0,2)$ is

  1. $20\hat{i} + 7\hat{j}$
  2. $20\hat{i} + 7\hat{j} + 12\hat{k}$
  3. $20\hat{i} + 12\hat{k}$
  4. $20\hat{i}$
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