1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Differentiation and tangent line

  1. Oct 26, 2011 #1
    1. The problem statement, all variables and given/known data
    Function
    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

    So,
    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

    User Avatar
    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:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook