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:
“To place oneself in the position of God is painful: being God is equivalent to being tortured. For being God means that one is in harmony with all that is, including the worst. The existence of the worst evils is unimaginable unless God willed them.”
—Georges Bataille (1897–1962)
“A strange effect of marriage, such as the nineteenth century has made it! The boredom of married life inevitably destroys love, when love has preceded marriage. And yet, as a philosopher has observed, it speedily brings about, among people who are rich enough not to have to work, an intense boredom with all quiet forms of enjoyment. And it is only dried up hearts, among women, that it does not predispose to love.”
—Stendhal [Marie Henri Beyle] (1783–1842)