Inflection Point - Equivalent Forms

Equivalent Forms

The following are all equivalent to the above definition:

  • a point on a curve at which the second derivative changes sign. This is very similar to the previous definition, since the sign of the curvature is always the same as the sign of the second derivative, but note that the curvature is not the same as the second derivative.
  • a point (x, y) on a function, f(x), at which the first derivative, f′(x), is at an extremum, i.e. a (local) minimum or maximum. (This is not the same as saying that y is at an extremum).
  • a point p on a curve at which the tangent crosses the curve at that point. For an algebraic curve, this means a non singular point where the multiplicity of the intersection at p of the tangent line and the curve is odd and greater than 2.

Read more about this topic:  Inflection Point

Famous quotes containing the words equivalent and/or forms:

    “I started off rapping for people just like myself, people who were in awe of wealth and flash. It was a conversation between me and them. But now most of those who buy my records are listening in on others’ conversation. They are the aural equivalent of voyeurs, thrilled at this crazy world that has nothing to do with their experience.”
    —Ice-T [Tracy Marrow], U.S. rap musician. Observer (London, Oct. 27, 1991)

    “The mind can make
    Substance, and people planets of its own
    With beings brighter than have been, and give
    A breath to forms which can outlive all flesh.”
    —George Gordon Noel Byron (1788–1824)