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 A scalar function in the $xy$-plane is given by $\phi \left ( x,y \right )=x^{2}+y^{2}$. If  $\hat{i}$ and $\hat{j}$ are unit vectors in the $x$ and $y$ directions, the direction of maximum increase in the value of $\phi$ at $(1,1)$ is along:

  1. $-2\hat{i}+2\hat{j}$
  2. $2\hat{i}+2\hat{j}$
  3. $-2\hat{i}-2\hat{j}$
  4. $2\hat{i}-2\hat{j}$
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