Point of inflection and symmetry

[pj33]

When is the point of inflection also poitn of symmetry? I mean i know it applies for even funcitons but, if a function has multiple points of inflection how can i know which is point of symmetry other than trying some values to check?
Also can does this apply to antisymmetry and odd functions?

 

[Dr.Peterson]

When is the point of inflection also point of symmetry? I mean i know it applies for even funcitons but, if a function has multiple points of inflection how can i know which is point of symmetry other than trying some values to check?
Also can does this apply to antisymmetry and odd functions?

Can you explain a little more about your own thinking? Are you basing the question on a particular example or two? Is there a particular problem you think this will help with?

An even function can't have a point of symmetry; the y-axis will be a line of symmetry, and it will pass through a local maximum or minimum, not a point of inflection. So it isn't clear what you mean by "it applies for even functions".

If a graph has a point of symmetry (that is, has point symmetry about a point on the graph), then if you translate it to put that point at the origin, it will be an odd function; and that point would be a point of inflection. (Each statement I'm making has some exceptions, and I'm ignoring them for simplicity.)

But most functions' graphs have no symmetry; this is not something to expect of a typical function.