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!

Homework Help: How to proove that that e^x is convex

  1. Oct 2, 2011 #1
    1. The problem statement, all variables and given/known data

    I have to determine if [e][/x] is a convex function. If it is then show proof. I know its a convex function by looking at the graph, Iam stuck at prooving it mathematically though.

    2. Relevant equations

    The function is f(x)=e^x.

    3. The attempt at a solution
    I am certain that the function is convex. I'am having trouble proving it though.

    Assuming we pick a point and call it x0, then a lies to the left of x0 and point b lies to the right.


    Once we substitute we get.

    I'am stuck at proving how this inequality is true.

  2. jcsd
  3. Oct 2, 2011 #2


    User Avatar
    Science Advisor

    If you are required to use the definition of "convex" then use the fact that
    [tex]e^{ta+ (1-t)b}= e^{ta}e^be^{-bt}[/tex]

    Or are you allowed to use the fact that a function is convex if and only if its second derivative is positive for all x?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook