Find the directions in which the function increases and decreases most rapidly at $P_0$. Then find the derivatives of the
function in these directions.
$f(x,y,z) = (x/y) - yz$, $P_0(1, 1, -4)$
The direction in which the given function $f(x,y,z) = (x/y) - yz$ increases most rapidly at $P_0(1, 1, -4)$ is
$\vec{u} = \boxed{}\vec{i} + \boxed{}\vec{j} + \boxed{}\vec{k}$.
(Type exact answers, using radicals as needed.)
The direction in which the given function $f(x,y,z) = (x/y) - yz$ decreases most rapidly at $P_0(1, 1, -4)$ is
$\vec{v} = \boxed{}\vec{i} + \boxed{}\vec{j} + \boxed{}\vec{k}$.
(Type exact answers, using radicals as needed.)
The derivative of the given function $f(x,y,z) = (x/y) - yz$ in the direction in which the function increases most rapidly at
$P_0(1, 1, -4)$ is $D_\vec{u}f = \boxed{}$.
(Type an exact answer, using radicals as needed.)
The derivative of the given function $f(x,y,z) = (x/y) - yz$ in the direction in which the function decreases most rapidly at
$P_0(1, 1, -4)$ is $D_\vec{v}f = \boxed{}$.
(Type an exact answer, using radicals as needed.)
