Question

Format: • If your answer below is a vector, input it as a column vector using the vector/matrix palette tool. • Use * to explicitly indicate multiplication between variables and other variables, between variables and brackets, or between sets of brackets (e.g. xy rather than xy; 2(x+y) rather than 2(x+y)). • Put arguments of functions in brackets (e.g. sin(x) rather than sin x). • Give your answers in exact form. Find the directional derivative of $f(x, y, z) = -14y^2z - 10y^2 + 4yz$ at P = $(4, -4, -2)$ in the direction of $(-7, -2, 1)$. $D_{(-7, -2, 1)}f|(4, -4, -2) =$ What is the maximum rate of increase of $f$ at P? $\nabla f|(4, -4, -2) = $

          Format:
• If your answer below is a vector, input it as a column vector using
the vector/matrix palette tool.
• Use * to explicitly indicate multiplication between variables and
other variables, between variables and brackets, or between sets
of brackets (e.g. x*y rather than xy; 2*(x+y) rather than 2(x+y)).
• Put arguments of functions in brackets (e.g. sin(x) rather than sin
x).
• Give your answers in exact form.
Find the directional derivative of $f(x, y, z) = -14y^2z - 10y^2 + 4yz$ at
P = $(4, -4, -2)$ in the direction of $(-7, -2, 1)$.
$D_{(-7, -2, 1)}f|(4, -4, -2) =$
What is the maximum rate of increase of $f$ at P?
$\nabla f|(4, -4, -2) = $

Format:
• If your answer below is a vector, input it as a column vector using
the vector/matrix palette tool.
• Use * to explicitly indicate multiplication between variables and
other variables, between variables and brackets, or between sets
of brackets (e.g. x*y rather than xy; 2*(x+y) rather than 2(x+y)).
• Put arguments of functions in brackets (e.g. sin(x) rather than sin
x).
• Give your answers in exact form.
Find the directional derivative of f(x, y, z) = -14y^2z - 10y^2 + 4yz at
P = (4, -4, -2) in the direction of (-7, -2, 1).
D(-7, -2, 1)f|(4, -4, -2) =
What is the maximum rate of increase of f at P?
∇ f|(4, -4, -2) =

Added by Denise G.

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