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!

Analysis: Inverse Function Theorem

  1. Nov 9, 2011 #1
  2. jcsd
  3. Nov 9, 2011 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    The function is monotone increasing, it does have an inverse even if the derivative happens to be zero at point. And you don't have to evaluate f'(pi/2) to solve the problem, you have to find f'(f^(-1)(-1)). What's f^(-1)(-1)?
     
  4. Nov 9, 2011 #3
    I know I'm not evaluating at that point. To me, it seems that the theorem states that for every x in the interval the derivative of the function cannot be zero. Pi/2 is in that interval.

    The answer to the problem is (c).
     
    Last edited: Nov 9, 2011
  5. Nov 9, 2011 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    That's not what it says. It's says f' has to be continuously differentiable and nonzero NEAR the point f^(-1)(-1). Not everywhere.
     
  6. Nov 9, 2011 #5

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Sure it is.
     
  7. Nov 9, 2011 #6
    What are you talking about? It says it right here.

    http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20111109_161232.jpg [Broken]

    I'm interpreting I = (0, 2pi).
     
    Last edited by a moderator: May 5, 2017
  8. Nov 9, 2011 #7

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You don't need to take I=(0,2pi). f^(-1)(-1)=pi, so take I=(pi-1/4,pi+1/4). Or any other small interval around pi that doesn't include pi/2. Then it fits your statement, doesn't it? That's what I mean by NEAR pi.
     
    Last edited by a moderator: May 5, 2017
  9. Nov 9, 2011 #8
    Yeah, I just realized that maybe setting that given interval equal to I is my problem. Thanks again.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Analysis: Inverse Function Theorem
Loading...