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Find f'(1), ∂g/∂s(1, 1), and ∂g/∂t(1,1).

  1. Apr 16, 2012 #1

    s3a

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    1. The problem statement, all variables and given/known data
    The problem is attached.

    The correct answers are:
    f'(1) = -68
    ∂g/∂s(1, 1) = 14
    ∂g/∂t(1, 1) = -136

    2. Relevant equations
    Differentiation and partial differentiation.

    3. The attempt at a solution
    I'm at the f'(1) part. I differentiated each component of F(2 – 3t + 2t^2, 19 – 27t + 9t^2, -4 + 3t + 2t^2) to get f'(t) = F(-3 + 4t, -27 + 18t, 3 + 4t) and then f'(1) = F(1, -9, 7). I'm not entirely certain if what I did is correct so far. If it is, what do I do next? If I omitted something important, tell me.

    Any help in solving this problem would be greatly appreciated!
    Thanks in advance!
     

    Attached Files:

  2. jcsd
  3. Apr 16, 2012 #2
    Looks fine to me.

    Now differentiate the components of g(s,t) first with respect to s, then with respect to t, and plug in (1, 1) just like before.
     
  4. Apr 16, 2012 #3
    Wait I misread this. Something is off...
     
  5. Apr 16, 2012 #4

    s3a

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    My answer differs from the correct answer quite a bit ;). Thanks anyways though.

    If someone else knows, please help me.
     
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