cal3
posted by Lucy .
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)>

p = √(4+1+1) = √6
u= p/p = (2/√6,1/√6,1/√6)
Now, with u = <0,1/√2,1/√2)>
∇<sub<uf = ∇f•u
= (y+z)(0) + (x+z)(1/√2) + (x+y)(1/√2)
= (0)(0)  1/√2 (2+1)  1/√2 (21)
= 4/√2 = 2√2 
Oh crap typo error, should read find the unit vector in direction of maximum increase of f in the direction of P.