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Homework Help: Max & Min

  1. Jan 7, 2009 #1
    1. The problem statement, all variables and given/known data

    let f(x)=(x+1)^2(x-2)
    a)Find the max and Min values of f(x)
    b)Find the inflection point of concavity

    2. Relevant equations

    using defferentiation



    3. The attempt at a solution
    for part a) differentiate (x+1)^2(x-2) we get ans=3(x-1)(x+1) Plse check for me?
    than f'(x)=0 therefore the points i got is x=1 and x=-1 respective??


    the second part not sure..plse assist.
     
  2. jcsd
  3. Jan 7, 2009 #2
    You are right about the local max and min. For the second part--all an inflection point is, is where the second derivative (that which we use to determine concavity) is 0. So you would have

    [tex]f''(x)=2(x-2)+4(x+1)=0[/tex]

    Can you get it from there?
     
  4. Jan 8, 2009 #3

    HallsofIvy

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    Science Advisor

    Make sure you answer the question asked! Max and Min occur at x= -1 and x= 1 but you haven't yet said what the max and min are.

    Also what jeffreydk said about the inflection point is slightly misleading. An inflection point is a point where the first derivative changes sign. That means the the second derivative must be 0 there but that is not sufficient. You need to check that the first derivative really does change sign. For example if f(x)= x4, f'= 4x3 and f"= 12x2. f"(0)= 0 but f' does NOT change sign there so (0,0) is NOT an inflection point of f(x)= x4.
     
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