Second derivative

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
 
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If it's positive on an interval, the function is convex there; if it's negative, the function is concave.
 
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.
 

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.
 
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http://online.math.uh.edu/Math1314/index.htm [Broken]

See section 11.
 
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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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