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:
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)
“All things will be produced in superior quantity and quality, and with greater ease, when each man works at a single occupation, in accordance with his natural gifts, and at the right moment, without meddling with anything else.”
—Plato (c. 427–347 B.C.)
“Walked forth to ease my pain
Along the shore of silver streaming Thames,
Whose rutty bank, the which his river hems,
Was painted all with variable flowers,”
—Edmund Spenser (1552?–1599)
“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)