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Gradient problem

  1. Mar 18, 2013 #1
    1. The problem statement, all variables and given/known data
    T(x,y,z)=8x^2-7xy+7xyz
    a. find the rate of change of t at point p(-1,1,-1) in the direction u=<8,10,-8>
    b. which direction does the temperature increase fastest
    c. find the maximum rate of increase at P.

    2. Relevant equations
    gradient of T=(16x-7y+7yz, -7x+7xz, 7xy)


    3. The attempt at a solution
    a. i multiplied gradient by unit vector <8,10,-8>/square root of 228 and i got -2.914
    please tell if this is right.
    b. i just found gradient T(-1,1,-1)=<-30,14,-7>
    c. i found the magnitude of b which was 33.84
     
  2. jcsd
  3. Mar 18, 2013 #2

    BruceW

    User Avatar
    Homework Helper

    yep, all good. Nice work.
     
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