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Find points of inflection from f''(x) = 12x + 18? A bit confused

  1. Mar 5, 2012 #1

    939

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    1. The problem statement, all variables and given/known data

    In my book it specifically asks to "find the points of inflection" of f (x) = 2x^3 + 9x^2 - 24x - 10.

    2. Relevant equations

    f (x) = 2x^3 + 9x^2 - 24x - 10
    f'(x) = 6x^2 + 18x - 24
    f''(x) = 12x + 18.

    3. The attempt at a solution

    What I don't get is why it asks for pointS. Isn't there just a single point here? Or can you get them not only by using the second derivative?

    I.e., set f"x = 0. Yet here only one point does that, not multiple ones? :S Could it be just a typo in the book?
     
  2. jcsd
  3. Mar 5, 2012 #2

    Mark44

    Staff: Mentor

    They are just asking the question in a general way, to include the possibility of multiple inflection points.
     
  4. Mar 5, 2012 #3

    939

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    That's what I was thinking, but why wouldn't they write point(s) or point/points then? :mad:. But yea you simply have to be right, I don't see how it's possible to find two from that...
     
  5. Mar 5, 2012 #4

    Mark44

    Staff: Mentor

    You're blowing a really minor thing way out of proportion. When they say "find the points of inflection ..." the possibilities are

    *no such points
    *one point
    *two or more points

    You should find something else to worry about.
     
  6. Mar 5, 2012 #5

    939

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    :blushing:
     
  7. Mar 5, 2012 #6

    Ray Vickson

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    Science Advisor
    Homework Helper

    I think the wording is their way of testing you. If they said inflection "point" that would be giving you a hint that there is only one. By saying "points" they are making you think about it.

    RGV
     
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