[Step-by-Step] Given f(x, y, z)=\mathrmx^2 \mathrmy^3 \mathrmz^6, in what direction is f(x, y, z) increasing the most rapidly at the point P(1,-1,1) ? What


Question: Given \(f(\mathrm{x}, \mathrm{y}, \mathrm{z})=\mathrm{x}^{2} \mathrm{y}^{3} \mathrm{z}^{6}\), in what direction is \(f(\mathrm{x}, \mathrm{y}, \mathrm{z})\) increasing the most rapidly at the point \(\mathrm{P}(1,-1,1) ?\) What is its rate of increase in that direction?

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