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:
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (1772–1834)
“A single spark can start a prairie fire.”
—Chinese proverb.
“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)
“When Western people train the mind, the focus is generally on the left hemisphere of the cortex, which is the portion of the brain that is concerned with words and numbers. We enhance the logical, bounded, linear functions of the mind. In the East, exercises of this sort are for the purpose of getting in tune with the unconscious—to get rid of boundaries, not to create them.”
—Edward T. Hall (b. 1914)