least and greatest value of function
Remark 1. If the preconditions of the theorem are fulfilled by a function , then one needs only to determine the values of in the end points and of the interval and in the zeros of the derivative inside the interval; then the least and the greatest value are found among those values.
Remark 2. Note that the theorem does not require anything of the derivative in the points and ; one needs not even the right-sided derivative in or the left-sided derivative in . Thus e.g. the function , fulfilling the conditions of the theorem on the interval but not having such one-sided derivatives, gains its least value in the end-point and its greatest value in the zero of the derivative.
Remark 3. The least value of a function is also called the absolute minimum and the greatest value the absolute maximum of the function.
|Title||least and greatest value of function|
|Date of creation||2013-03-22 15:38:57|
|Last modified on||2013-03-22 15:38:57|
|Last modified by||pahio (2872)|
|Synonym||global extrema of real function|