Point P is a point of inflection?

[Hootenanny]

I just want to check something I'm not sure on. If at point P; $f'(x) = 0$ and $f''(x) = 0$ and $f'''(x) \neq 0$ can we definatly say that point P is a point of inflection?

Regards,
~Hoot

 

[Hootenanny]

"bump"

 

[Zurtex]

That depends how you define "point of inflection", some times that's just how it is defined.

Easy way to test, if you consider x⁵ to be a point of inflection at x=0 then your test fails.

However if you don't consider it to be a point of inflection then your test is fine.

 

[Hootenanny]

Thank you Zurtex, extremely helpful.

Regards,
~Hoot