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Math Help - Find interval of function

  1. #1
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    Find interval of function

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  2. #2
    Newbie madmartigano's Avatar
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    Inflection points occur where f\prime \prime (x) = 0

    If f\prime \prime (x) = 0 at x = -1 and x = 3, for example,
    then your intervals are ( - \infty , - 1), ( - 1,3), (3, + \infty )

    You can determine the concavity of an interval by checking any value within that interval using f\prime \prime (x)

    For the interval ( - \infty , - 1), you could use the number -10

    If f\prime \prime (-10) is positive, then that interval is concave up.

    If f\prime \prime (-10) is negative, then that interval is concave down.

    Also, if f\prime \prime (x) is negative on both sides or positive on both sides, then there is no inflection point at x.

    \begin{array}{l}<br />
 f(x) = {x^4} - 4{x^3} \\ <br />
 f\prime (x) = 4{x^3} - 12{x^2} \\ <br />
 f\prime \prime (x) = 12{x^2} - 24x = 12x(x - 2) \\  \end{array}
     f\prime \prime (x) = 0 @  x = 0, 2 \\

    Can you figure it out from there?
    Last edited by madmartigano; March 8th 2009 at 09:24 PM.
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