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Let $z = f(x,y)$ be the differentiable function given implicitly by $x^3 +y^3 +z^3 + xyz =9$ and such that $f(0,1)=2$.

  1. Find $\nabla f$ at the point $P_0 = (0, 1)$.
  2. Find the rate and direction of the steepest increase of $f$ at $P_0$.
  3. Find $(D_u f)(P_0)$, where $u = (\mathbf{i}+\mathbf{j})/\sqrt{2}$.
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    actually i know the whole process when the given function is not implicit, however, i could not understand how should i do when it is implicit2012-10-30

2 Answers 2