This questicont $1$ points$)$ poss ble

Find unit vectors in the directions in which the function f increases and decreases most rapidly at $P_0.$ Then find the directional derivatives of the function in those directions.

$f(x,y,z)=4ln(xy)ln(yz)3ln(xz),P_0(1,1,1)$

The function increases most rapidly in the direction of the unit vector

$u=i,|i|ji|k|$

$($Simplify your answers. Type exact answers, using radicals as needed. Do not rational$/$re any denominators$)$

The function decreases most rapidly in the drection of the unit

$-u=,ii,ik$

$($Smplify your answers. Type exact answers, using radicals as needed Do not rationalure any denominators$)$

The directional derivative in the direction of $u$ is $(D_u)p_0=$

$($Simplify your answer. Type an exact answer, using radicals as needed$)$

The directional derivative in the direction of $-u$ is $(D_{-u})p_e=q,$

$($Simplify your answer. Type an exact answer, using radicals as needed.$)$

Time Remaining; $00$:$31$:

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