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3. [2/3 Points] DETAILS PREVIOUS ANSWERS SCALCET9M 14.6.012. Consider the following. f(x, y, z) = y$^2$e$^{xyz}$, P(0, 3, -3), u = $\begin{pmatrix} \frac{12}{13} & \frac{3}{13} & \frac{4}{13} \end{pmatrix}$ (a) Find the gradient of f. $\nabla$f(x, y, z) = $\begin{pmatrix} y^3ze^{xyz} & e^{xyz}(xy^2z + 2y) & xy^3e^{xyz} \end{pmatrix}$ (b) Evaluate the gradient at the point P. $\nabla$f(0, 3, -3) = (-81, 6, 0) (c) Find the rate of change of f at P in the direction of the vector u. D$_u$f(0, 3, -3) = $-\frac{948}{13}$

          3. [2/3 Points]
DETAILS
PREVIOUS ANSWERS
SCALCET9M 14.6.012.
Consider the following.
f(x, y, z) = y$^2$e$^{xyz}$, P(0, 3, -3), u = $\begin{pmatrix} \frac{12}{13} & \frac{3}{13} & \frac{4}{13} \end{pmatrix}$
(a) Find the gradient of f.
$\nabla$f(x, y, z) = $\begin{pmatrix} y^3ze^{xyz} & e^{xyz}(xy^2z + 2y) & xy^3e^{xyz} \end{pmatrix}$
(b) Evaluate the gradient at the point P.
$\nabla$f(0, 3, -3) = (-81, 6, 0)
(c) Find the rate of change of f at P in the direction of the vector u.
D$_u$f(0, 3, -3) = $-\frac{948}{13}$

3. [2/3 Points]
DETAILS
PREVIOUS ANSWERS
SCALCET9M 14.6.012.
Consider the following.
f(x, y, z) = y^2e^xyz, P(0, 3, -3), u = < p m a t r i x >
(a) Find the gradient of f.
∇f(x, y, z) = < p m a t r i x >
(b) Evaluate the gradient at the point P.
∇f(0, 3, -3) = (-81, 6, 0)
(c) Find the rate of change of f at P in the direction of the vector u.
Duf(0, 3, -3) = -(948)/(13)

Added by Ashley H.

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