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:
“Every notable advance in technique or organization has to be paid for, and in most cases the debit is more or less equivalent to the credit. Except of course when it’s more than equivalent, as it has been with universal education, for example, or wireless, or these damned aeroplanes. In which case, of course, your progress is a step backwards and downwards.”
—Aldous Huxley (1894–1963)
“While waiting to get married, several forms of employment were acceptable. Teaching kindergarten was for those girls who stayed in school four years. The rest were secretaries, typists, file clerks, or receptionists in insurance firms or banks, preferably those owned or run by the family, but respectable enough if the boss was an upstanding Christian member of the community.”
—Barbara Howar (b. 1934)