Proving points of inflection

[brightsky]

Yeah, does the second derivative method work with graphs like ? The (0,0) won't be a point of inflection right?

[brightsky]

Just a good example for you brightsky, take the graph
It has a point of inflection at the origin, but it is not stationary, as the gradient at the point is not zero.

Yeah, we've been learning all about stationary point of inflections at Dr He, so I've become a bit disillusioned by the general definition of point of inflection. :p

[the.watchman]

Yeah, does the second derivative method work with graphs like ? The (0,0) won't be a point of inflection right?

For etc., the origin is a point of inflection, but it is a special type, a stationary point of inflection

[Yitzi_K]

Try your method (without a gradient check on both sides) on . I (think) this gives the answer to the thread =T (note: have not done any Maths whatsoever in 2 years, might be wrong with the definitions here)

2nd derivative gives therefore PoI is 0... but this quartic has no PoI, it's a stationary point.

I get what you're saying. Thanks. I'd karma you if I could

[brightsky]

Yeah, does the second derivative method work with graphs like ? The (0,0) won't be a point of inflection right?

For etc., the origin is a point of inflection, but it is a special type, a stationary point of inflection

Really? The concavity doesn't really change though?

[the.watchman]

Yeah, does the second derivative method work with graphs like ? The (0,0) won't be a point of inflection right?

For etc., the origin is a point of inflection, but it is a special type, a stationary point of inflection

Really? The concavity doesn't really change though?

True, now I'm confused, is a stationary point of inflection a point of inflection? :idiot2:

[brightsky]

Nah, don't think it's a point of inflection at all. As Yitzi_K said, it's just a stationary point.

[shinny]

Yeah, does the second derivative method work with graphs like ? The (0,0) won't be a point of inflection right?

For etc., the origin is a point of inflection, but it is a special type, a stationary point of inflection

Really? The concavity doesn't really change though?

True, now I'm confused, is a stationary point of inflection a point of inflection? :idiot2:

It is, when it's actually a point of inflection. It's not in the case of though; it's clearly just a turning point. Just a nice, simple example to show why you must do a gradient check I guess.

[the.watchman]

Nah, don't think it's a point of inflection at all. As Yitzi_K said, it's just a stationary point.

But it is called a stationary ... oh crap you're right, it's just a stationary point / turning point
I'm an idiot =='

I got stationary points and SPOIs muddled :uglystupid2: