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: Local maxima and minima

  1. Mar 30, 2012 #1
    1. The problem statement, all variables and given/known data
    Find critical points
    Find local maxima & minima

    2. Relevant equations

    3. The attempt at a solution
    F'(x) = x(x+2)/(x+1)^2

    crit points: -2,0,-1

    f(-2) = -4
    f(0) = 0

    My book is telling me that f(0) is the minima, and f(-2) is the maxima. I see it as the other way around. Which way is right? Explanations? Thank you!
  2. jcsd
  3. Mar 30, 2012 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    The book is correct.

    I suppose you're having trouble because the local maximum is less than the local minimum.

    Graph F(x) to see what's happening .
  4. Mar 31, 2012 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    The book is correct. For *local* min/max (as you have here) there are second-order conditions that can be applied: if f'(x0) = 0 and f''(x0) < 0 then x0 is a strict local maximum; if f'(x0) = 0 and f''(x0) > 0, x0 is a strict local minimum. Try these tests on your function.

    This does not say anything about *global* max or min, and it does not prevent a local max from being less than a local min, which is the case in this problem.

  5. Mar 31, 2012 #4
    I'd like to thank you both for your guidance. I will be looking into this further.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook