Find intervals where the graph of the function f(x)= x^3-9x is concave up or concave down and all inflection points.

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The intervals where a function is concave up is where the second derivative is positive, and it is concave down when the second derivative is negative.




We see that the second derivative is positive when `x>0` and negative when `x<0` .  This also means that there is only one inflection point at (0,0).

The function has an inflection point at (0,0), is concave up for `x>0` and concave down for `x<0` .

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