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cal3

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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 - ,

    |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 (2-1)
    = -4/√2 = -2√2

  • cal3 - ,

    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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