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!

F''(x)>0 in [a,b] so f has a maximum at a or b.

  1. Dec 31, 2012 #1
    Hi,
    1. The problem statement, all variables and given/known data
    I was asked to show that if f''(x)>0 for every x in [a,b], then f has a maximum at either a or b.


    2. Relevant equations



    3. The attempt at a solution
    The book proves it thus:
    If f has a sationary point in [a,b] then that point must be a minimum, as f''(x)>0, hence a maximum must be obtained at either a or b.
    If f does not have a stationary point in [a,b], then f is increasing or decreasing in [a,b] and hence a maximum must be obtained at either a or b.

    I don't understand both "hence a maximum must be obtained at either a or b" and "then f is increasing or decreasing in [a,b] and hence a maximum must be obtained at either a or b".
    Could someone please clarify?
     
  2. jcsd
  3. Dec 31, 2012 #2
    I believe I've got it, thanks anyway :-)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook