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Quick help!

  1. Apr 6, 2008 #1
    ok. So if the second derivative of a function is equal to a constant and i want to find any intervals of concavity there is none right? therefore no infelction points nor relative and/or absolute extrma

    f(second derivative)(x)=2
     
  2. jcsd
  3. Apr 7, 2008 #2

    CompuChip

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    A function is called concave if the second derivative is negative. So if f'' is constant, then it is everywhere either concave, or convex (or f'' = 0). Inflection points are those where the derivative changes sign, so indeed there are none. The extrema have to do with the first derivatives of the function. For example, I can make up a function f(x) such that f''(x) = 2 but which has a global minimum... can you?
     
  4. Apr 7, 2008 #3

    HallsofIvy

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    For example, f(x)= x2 has second derivative 2 and is convex for all x and has 0 as an absolute minimum.

    f(x)= -x2 has second derivative -2 and is concave for all x and has 0 as an absolute maximum.

    Of course, neither of those has any inflection points.
     
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