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Local maxima and minima

  1. Mar 30, 2012 #1
    1. The problem statement, all variables and given/known data
    F(x)=(x^2)/(x+1)
    Find critical points
    Find local maxima & minima

    2. Relevant equations
    None

    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
    f(-1)=undef

    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

    SammyS

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    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

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    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.

    RGV
     
  5. Mar 31, 2012 #4
    I'd like to thank you both for your guidance. I will be looking into this further.
     
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