# Is 'vertex' the correct term for peak (and valley) point on a curve?

This is about mathematical terminology in English.

A simple curving line can have a top peak and a bottom valley. What is the correct term to use for the top/bottom point?

In my native tongue, we call it a `toppunkt`, literally meaning `top-most point` (although it counts for both peaks and valleys). When looking it up I have found the word `vertex`, which Wikipedia agrees with. Is this really the correct term?

Oxford Dictionaries doesn't seem to agree but only defines `vertex` as opposite angular points in a geometrical shape.

`Vertex` literally means `turning point` in Latin, so it does make sense. But from simple google searches, the word `vertex` doesn't seem to be used very often and the term `turning point` actually seems to be used as well.

I would appreciate help with sorting out the terminology here.

Note that I am aware that such a point is called a `stationary point` in 2D (and higher dimensions). I am specifically asking to the 1D case, though, where there is a special term.

This is quite technical mathematical language, the vertex, or apex is the point at which the curvature is a minimum or a maximum. For a vertical parbola, the vertex occurs at the maximum point. For a car driver, the apex of a turn is the point at which the steering wheel is turned the most.

However, it is more common to speak of

• a "stationary point" (zero gradient, applies to 1D as well higher dimensions),
• a "turning point" (a stationary point that isn't an inflexion) or
• a "(local) maximum/minimum" (which will be at a stationary point, if the curve is differentiable)

"Turning point" is the most useful term for the top or bottom of a curve.

Find the turning points of the curve y = x³ - x, and for each point, determine if it is a maximum or minimum.

• Thank you for the answer. So, you would advise me to use the term `turning point` in technical work rather than `vertex` or `apex`? Or is it a "colloquial" term? Regarding your first point, I am aware of the term `stationary point` which my native language also uses - but of some reason we never use that term in the 1-dimensional case although it strictly is correct. Not even in technical literature. Instead we have the term `toppunkt` to use for 1D. I am assuming that this is also the case in English - but please correct me if wrong - and I am thus looking for the translation of `toppunkt`. – Steeven May 14 '19 at 8:21
• If you're talking about a sine wave or similar the usual terms would be "peak" and "trough." Turning point is used as a technical term, along with (local) maxima and (local) minima. – Showsni May 14 '19 at 15:29