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!

Functions with increasing derivatives

  1. Nov 18, 2013 #1
    Consider a function f(x), such that for all points x0 in the domain, the nth derivative of f evaluated that x0 is less than the n+1th derivative of f evaluated at x0.

    A quick example is f(x) = e^(ax) where a > 1, what others are there (not including just changing e to something else)? Is there a name for these?
     
  2. jcsd
  3. Nov 18, 2013 #2

    AlephZero

    User Avatar
    Science Advisor
    Homework Helper

    It's easy to invent infinite power series that have this property. For example ##f(x) = 0 + x + 2x^2 + 3x^3 + \dots##.

    Proving (a) it has the required property and (b) it is convergent (for some real values of ##x##) are left as exercises for the OP.

    Actually, you don't need the infinite series. ##f(x) = -1/x##, when ##-1 < x < 0##.
     
    Last edited: Nov 18, 2013
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Functions with increasing derivatives
  1. Functional Derivative (Replies: 0)

Loading...