1. Limited time only! Sign up for a free 30min personal 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!

Finding f inverse prime at a point c

  1. Nov 3, 2012 #1
    1. The problem statement, all variables and given/known data
    Assume the function f defined by f(x)=5x+sin(πx) is strictly increasing on ℝ. Find (f[itex]^{-1}[/itex])'(10)


    2. Relevant equations
    Let I and J be be intervals and let f:I->J be a continuous, strictly monotone function. If f is differentiable at c and if f'(c)≠0, then (f[itex]^{-1}[/itex]) is differentiable at f(c) and (f[itex]^{-1}[/itex])'(f(c))= 1/f'(c)


    3. The attempt at a solution

    It is clear f is continuous and differentiable on ℝ.
    => f'(x) = 5+πcos(πx)


    Finding when f(x)=10,
    10 = 5x+sin(πx) => x=2

    Then (f[itex]^{-1}[/itex])'(f(2))=1/f'(2) = 1/(5+πcos(2π)) = 1/(5+(π))

    Is this how to do it, or do I use f(10) instead of finding when f(x) is 10?
     
  2. jcsd
  3. Nov 4, 2012 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    That all looks right. If you think of it as y = f(x) and x = f-1(y), the 10 is a value of y, not of x, so f(10) and f'(10) would not be relevant.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook