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Second derivative

  1. Apr 19, 2007 #1
    I would like someone to tell me what is the geometric interpretation of the second derivative at a fixed point, or in an interval??

    thx
     
  2. jcsd
  3. Apr 19, 2007 #2
    If it's positive on an interval, the function is convex there; if it's negative, the function is concave.
     
  4. Apr 19, 2007 #3
    Second derivative is the rate of change of the derivative, i.e "how fast is the gradient changing?".
    Say the second derivative is 1 at point A and 2 at point B on the same function. Then the gradient (the derivative) is changing faster at point A than point B.
     
  5. Apr 19, 2007 #4

    mathwonk

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    it measures curvature, or concavity, tells whether it is up or down, and how sharply.

    it also determines whether the tangent line is above or below the graph.
     
    Last edited: Apr 19, 2007
  6. Apr 19, 2007 #5
  7. Apr 20, 2007 #6
    i guess i already knew this,just did not actually think about it.
    However, if this is what i was looking for, i will see later when i think more about it, and if i still have problems i will come back.

    Thankyou guys, for giving me some flash back
     
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