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The greatest rate of increase of \(f=xy^2z^3\) at the point \((0,-1,-2)\) is :

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The maximum directional derivative of a function is always equal to the magnitude of the gradient vector: \[ D_{\max}f=|\nabla f| \] The gradient direction always gives the direction of steepest increase.

Updated On: May 22, 2026

\(4\)
\(8\)
\(10\sqrt{2}\)
\(-8i\)

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The Correct Option is B

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The greatest rate of increase of \(f=xy^2z^3\) at the point \((0,-1,-2)\) is :

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The Correct Option is B

Solution and Explanation

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