The second directional derivative of $f(x, y)$ is $D_u^2f(x, y) = D_u[D_uf(x, y)]$. If $f(x, y) = x^3 + 5x^2y + y^3$ and $u = \begin{pmatrix} 3/5 \\ 4/5 \end{pmatrix}$, calculate $D_u^2f(2, 3)$. $D_u^2f(2, 3) = 80.3$
Added by Miriam H.
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∇f(x, y) = (3x² + 10xy, 5x² + 3y²) Show more…
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The $ \textbf{second directional derivative} $ of $ f(x, y) $ is $$ D_u^2 f(x, y) = D_u [ D_u f(x, y) ] $$ If $ f(x, y) = x^3 + 5x^2y + y^3 $ and $ u = \langle \frac{3}{5}, \frac{4}{5} \rangle $, calculate $ D_u^2 f(2, 1) $.
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