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Where is x^3 + 12x + 5 increasing and decreasing

  1. Feb 13, 2006 #1
    Find intervals on which f(x)=-x^3 + 12x +5 , -3<x<3 is increasing and decreasing. Where does the function assume extreme values and what are these values ?

    does anybody knows how to do this??
     
  2. jcsd
  3. Feb 13, 2006 #2

    TD

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    I have the feeling derivatives may be a good idea :smile:

    Do you know a necessary and/or sufficient condition for extrema, using derivatives?
     
  4. Feb 13, 2006 #3
    no,pls explain to me
     
  5. Feb 13, 2006 #4

    TD

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    When a function becomes extreme in a point, the tangent line will be horizontal there which means that the derivative of the function is 0 there. Note that this is a one-way argument, an extremum implies a zero derivative but not the other way arround, so this is a necessary condition - though not sufficient.

    To check whether it is actually a min or max, you can use the second derivative or investigate whether the function switches from increasing to decreasing or vice versa arround that point.
     
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