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Homework Help: Differentiation and tangent line

  1. Oct 26, 2011 #1
    1. The problem statement, all variables and given/known data
    f(x) = KxL

    K= 1.78
    L= -1.39
    Problem 1: Find f'(x).
    v= 0.89
    w= 0.5
    "v" and "w" are two points located on the x-axis.
    Problem 2: Calculate f'(v).
    Problem 3: Find the equation of the tangent line of f(x) over the point "w". The equation should be in this form y=Ax+B

    Problem 1:This is how I worked out the differentiation:
    f(x) = e(ln 1.78)x-1.39
    Setting u=x-1.39,
    f'(x) = (Ku)'(u) * u'

    (Ku)'(u) = (eu ln K)' = ln K * eu ln K = ln K * Ku
    u' = LxL-1 = -1.39x-2.39

    f'(x) = ln 1.78(1.78x-1.39) * -1.39x-2.39

    Is this correct?
    Regarding the other problems, do I need f'(x) to solve these? I don't know where to start.
    Last edited: Oct 26, 2011
  2. jcsd
  3. Oct 26, 2011 #2

    I like Serena

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    Homework Helper

    Hi again LizzieL! :smile:

    Yes. Your expression for f'(x) is correct!

    For problem 2 you'd simply substitute v=0.89 for x in f'(x).

    For problem 3 you need to substitute w=0.5 for x in f(x) and in f'(x).
    After that you need to find A and B such that f'(w) = A and f(w) = Aw + B.
  4. Oct 26, 2011 #3
    I got it! Thanks :approve:
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