Point of inflection definition

[horizon]

Hi,

To find the points of inflection, I've been told to let f double dashed x equal to zero and solve for that.  Do you, however (in addition to this), have to check the second derivative on either sides of the x values to verify that there is indeed a change in concavity?
Will, for example, f double dashed x=0 at times NOT give points of inflection? If so, does anyone have an example of this?

Thanks!!!!!!!!!!!

[TrueTears]

there are 3 types of points of inflexion, when f'(x) > 0 and f''(x) = 0. f'(x) < 0 and f''(x) = 0. f'(x)= 0 and f'''(x), the latter being called a stationary point of inflexion

[luffy]

there are 3 types of points of inflexion, when f'(x) > 0 and f''(x) = 0. f'(x) < 0 and f''(x) = 0. f'(x)= 0 and f'''(x), the latter being called a stationary point of inflexion

I think you meant the third one to be f'(x) = 0 and f''(x) = 0?

Will, for example, f double dashed x=0 at times NOT give points of inflection? If so, does anyone have an example of this?

E.g. y = x^4. This function often shows the exceptions to those f''(x) rules.

Hope I helped.

[TrueTears]

yeh both 0