Inflection Point Without Sign Change

1. The problem statement, all variables and given/known data



Find the points of inflection of y. (See picture for y).







2. Relevant equations



Inflection points occur where the concavity of the graph changes. This means the sign of f''(x) changes.



However, the sign of f''(x) does not change around -sqrt8. I confirmed this with Wolfram Alpha by having it take the second derivative and having it find the value of the second derivative at points around the points that would zero the second derivative.



Nonetheless, Wolfram Alpha insists that -sqrt8 is a point of inflection.



What's up?



WA page for reference below. Note that it says -sqrt8 and sqrt8 are inflection points. :confused:



http://www.wolframalpha.com/input/?i...+%2B+8%2Fx%5E3



This is the computed second derivative.



http://www.wolframalpha.com/input/?i...+%2B+8%2Fx%5E3



We can see this second derivative is positive for BOTH x = -3 and x = 1. Note that -3 < -sqrt8 < 1.



http://www.wolframalpha.com/input/?i...x+%3D+%28-3%29



http://www.wolframalpha.com/input/?i...5E5+at+x+%3D+1

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