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!

B Proving these two functions intersect at 'a'

  1. Sep 25, 2016 #1
    Through experimental observations, I have found that the two functions ##f\left(x\right)=x^{a\left(a-x^3\right)}-a## and ##g\left(x\right)=a^{x\left(x-a^3\right)}-x## will always intersect at ##a## when ##x>0##. Is there a way to mathematically prove this? For instance, simultaneously solving the functions and simplifying the answer down to ##x=a## (Note: the functions sometimes also intersect at other locations besides ##[a, f(a)]##)
     
  2. jcsd
  3. Sep 25, 2016 #2

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You mean prove that ##f(a) = g(a)##?
     
  4. Sep 25, 2016 #3
    Ah yes, expressing it that way does seem a lot clearer.
     
  5. Sep 25, 2016 #4

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Isn't that obvious if you just plug in a for x?
     
  6. Sep 25, 2016 #5
    Right, so it was midnight when I posted this and I wasn't in the most clear mindset. Looking back on this now I can see that by proving ##f(a)=g(a)## you also prove that ##f(x)## intersects ##g(x)## at ##x=a##. Sorry for this entire post.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Proving these two functions intersect at 'a'
Loading...