Posted by **Lucy** on Monday, February 27, 2012 at 12:58am.

Consider the function f(x,y)=xy+xz+yz+4 at point p=(2,-1,1)

a)find the unit vector in direction of p.

b) find the directional derivative at p in the direction of <0,-1/(sqrt2),-1/(sqrt2)>

- cal3 -
**Steve**, Monday, February 27, 2012 at 12:52pm
|**p**| = √(4+1+1) = √6

**u**= **p**/|**p**| = (2/√6,-1/√6,1/√6)

Now, with **u** = <0,-1/√2,-1/√2)>

∇<sub<**u**f = ∇f•**u**

= (y+z)(0) + (x+z)(-1/√2) + (x+y)(-1/√2)

= (0)(0) - 1/√2 (2+1) - 1/√2 (2-1)

= -4/√2 = -2√2

- cal3 -
**Lucy**, Monday, February 27, 2012 at 7:07pm
Oh crap typo error, should read find the unit vector in direction of maximum increase of f in the direction of P.

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