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Homework Help: Find Points of Inflection

  1. Oct 21, 2011 #1
    1. The problem statement, all variables and given/known data

    Find the points of inflection of the graph of the function. (If an answer does not exist, enter DNE.)

    2. Relevant equations
    f(x)=1/3x^4 + 4x^3

    3. The attempt at a solution
    Found f'(x)= x^2(4/3x+12)
    Also found critical numbers to x=0 and x=-9

    I don't know how to get point of inflection
  2. jcsd
  3. Oct 21, 2011 #2


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    Science Advisor
    Homework Helper

    Points of inflection are where the function changes concavity. They are related to second derivatives, aren't they? Look it up.
  4. Oct 21, 2011 #3
    For inflection points:
    Find the second derivative of the function and set it equal to zero.

    I found that that x=-6 and x=0.

    Test some points right and left of the second derivative zeros (^) to confirm concave up or concave down. A positive value is concave up, vice versa :)
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