Definition For Single Variable Functions
A critical point of a function of a single real variable, ƒ(x), is a value x0 in the domain of ƒ where either the function is not differentiable or its derivative is 0, ƒ′(x0) = 0. Any value in the codomain of ƒ that is the image of a critical point under ƒ is a critical value of ƒ. These concepts may be visualized through the graph of ƒ: at a critical point, either the graph does not admit a tangent or the tangent is a vertical or horizontal line. In the last case, the derivative is zero and the point is called a stationary point of the function.
Read more about this topic: Critical Point (mathematics)
Famous quotes containing the words definition, single, variable and/or functions:
“It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
—Jane Adams (20th century)
“A single gentle rain makes the grass many shades greener. So our prospects brighten on the influx of better thoughts.”
—Henry David Thoreau (1817–1862)
“There is not so variable a thing in nature as a lady’s head-dress.”
—Joseph Addison (1672–1719)
“Adolescents, for all their self-involvement, are emerging from the self-centeredness of childhood. Their perception of other people has more depth. They are better equipped at appreciating others’ reasons for action, or the basis of others’ emotions. But this maturity functions in a piecemeal fashion. They show more understanding of their friends, but not of their teachers.”
—Terri Apter (20th century)