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Inflection help

  1. Dec 28, 2007 #1
    Hi, can someone help me guide me on how to find inflections? I am not too sure how to do it in such a problem as the follows:

    1. The problem statement, all variables and given/known data
    Determine a, b, and c so that the function
    f(x) = x^3 + ax^2 + bx + c has critical points at (1,5) and an inflection point at (2,3)


    2. Relevant equations



    3. The attempt at a solution

    I am not too sure how to persue this, for critical points I know the derivative needs to equal zero and then you find the critical points that way, but I dont know what to do for the inflection.
    Thank You!
     
  2. jcsd
  3. Dec 28, 2007 #2
    1st derivative - critical points

    2nd derivative - inflection points
     
  4. Dec 28, 2007 #3
    Yep, thanks I figured it out
    a = -9/2
    b = 11

    But I cant find out what c is;
    This is wat I did by the way;

    y = x3 + ax2 + bx + c

    y' = 3x2 + 2ax + b

    y'' = 6x + 2a

    Take y' and plug in (1, 5)

    5 = 3(1) + 2a(1) + b ==> 2a + b = 2 ............ (1)

    Take y'' and plug in (2, 3)

    3 = 6(2) + 2a ==> a = -9/2 ............... (2)

    Then, plug (2) into (1) to find b

    b = 11
     
  5. Dec 28, 2007 #4
    The points (1,5), (2,3) are [tex] (x,y) [/tex] points not [tex](x,y')[/tex] or [tex](x,y'')[/tex] points!

    On critical points [tex]y'(x_o)=0[/tex]

    On inflection points [tex]y''(x_o)=0[/tex]
     
  6. Dec 28, 2007 #5
    Ohh, ok, yes, I fixed it now, I have my answer to be

    a = -6
    b = 9
    c = 1
     
  7. Dec 28, 2007 #6
    And that's the correct one! :smile:
     
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