Find the directions in which the function increases and decreases most rapidly at Po. Then find the derivatives of the function in these directions.
$f(x,y,z) = \frac{x}{y} - yz$,
$P_0(-2, -1, -4)$
The direction in which the given function $f(x,y,z) = \frac{x}{y} - yz$ increases most rapidly at $P_0(-2, -1, -4)$ is $u = \square i + \square j + \square k$.
(Type exact answers, using radicals as needed.)
The direction in which the given function $f(x,y,z) = \frac{x}{y} - yz$ decreases most rapidly at $P_0(-2, -1, -4)$ is $v = \square i + \square j + \square k$.
(Type exact answers, using radicals as needed.)
The derivative of the given function $f(x,y,z) = \frac{x}{y} - yz$ in the direction in which the function increases most rapidly at $P_0(-2, -1, -4)$ is $D_uf = \square$.
(Type an exact answer, using radicals as needed.)
The derivative of the given function $f(x,y,z) = \frac{x}{y} - yz$ in the direction in which the function decreases most rapidly at $P_0(-2, -1, -4)$ is $D_vf = \square$.
(Type an exact answer, using radicals as needed.)
