EXTREME POINT Meaning and
Definition
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An extreme point, also known as a corner point, refers to a critical point in mathematics that represents either the maximum or minimum value of a function. In the field of optimization, it signifies the endpoints or boundaries of a feasible region, where the function attains its most extreme values.
In a two-dimensional plane, an extreme point is typically found at the intersection of two or more linear constraints that define the feasible region. At this point, the function's value cannot be improved by moving within the region. Mathematically, an extreme point is determined by identifying the values of the variables that satisfy all the given constraints simultaneously.
In higher dimensions, such as in a three-dimensional space, an extreme point is defined as the intersection of multiple planes or surfaces that form the feasible region. These points exhibit the highest or lowest values of the objective function within the region.
Extreme points are essential in optimization problems as they help find the optimal solution. By connecting extreme points, one can construct a convex hull, which outlines the overall shape of the feasible region. This convex hull facilitates the identification of the global maximum or minimum of the function by investigating the extreme points. Consequently, extreme points play a crucial role in various disciplines, including mathematics, economics, and engineering, by assisting in determining the most advantageous or efficient solutions to optimization problems.
Common Misspellings for EXTREME POINT
- wxtreme point
- sxtreme point
- dxtreme point
- rxtreme point
- 4xtreme point
- 3xtreme point
- eztreme point
- ectreme point
- edtreme point
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- exrreme point
- exfreme point
- exgreme point
- exyreme point
- ex6reme point
- ex5reme point
- exteeme point
- extdeme point
- extfeme point
- extremepoint
Etymology of EXTREME POINT
The word "extreme" originated from the Latin word "extremus", which means "outermost" or "farthest". It is derived from the prefix "ex-" (meaning "out") and the root "ter" (meaning "earth" or "land"). The term "point" comes from the Latin word "punctum", meaning "something that is prickled or pricked". When combined, "extreme point" refers to the outermost or farthest position or location, often used in mathematical or geographical contexts.
Similar spelling words for EXTREME POINT
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