what is a minimum and maximum

what is a minimum and maximum In mathematical analysis the maximum and minimum a of a function are respectively the largest and smallest value taken by the function Known generically as extremum b they may be defined either within a given range the local or relative extrema or on the entire domain the global or absolute extrema of a function

Global or Absolute Maximum and Minimum The maximum or minimum over the entire function is called an Absolute or Global maximum or minimum Assuming this function continues downwards to left or right The Global Maximum is about 3 7 There is no Global Minimum as the function extends infinitely downwards Calculus A high point is called a maximum plural maxima A low point is called a minimum plural minima The general word for maximum or minimum is extremum plural extrema We say local maximum or minimum when there may be

what is a minimum and maximum

what is a minimum and maximum
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Identify The Vertex Of The Graph Tell Whether It Is A Minimum Or
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Maximums And Minimum
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As x f x Therefore the function does not have a largest value However since x2 1 1 for all real numbers x and x2 1 1 when x 0 the function has a smallest value 1 when x 0 We say that 1 is the absolute minimum of f x x2 1 and it occurs at x 0 Definition We say that f x f x has an absolute or global maximum at x c x c if f x f c f x f c for every x x in the domain we are working on We say that f x f x has a relative or local maximum at x c x c if f x f c f x f c for every x x in some open interval around x c x c

Minimum means the least you can do of something For example if the minimum amount of dollars you must pay for something is seven then you cannot pay six dollars or less you must pay at least seven You can do more than the minimum but no less Maximum means the most you can have of something Maximums and Minimums Calculus College What is a local maximum A local maximum is a point where the function is larger at that point than it is in either direction That is for both slightly smaller and slightly larger values of x x the function is smaller

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Although f 0 f 0 is not the largest value of f f the value f 0 f 0 is larger than f x f x for all x x near 0 We say f f has a local maximum at x 0 x 0 Similarly the function f f does not have an absolute minimum but it does have a local minimum at x 1 x 1 because f 1 f 1 is less than f x f x for x x near 1 What Is Local Maximum and Minimum The local maxima and minima are the input values for which the function gives the maximum and minimum output values respectively The function equation or the graphs are not sufficiently useful to find the local maxima and local minima points

If x f x x f x is a point where f x f x reaches a local maximum or minimum and if the derivative of f f exists at x x then the graph has a tangent line and the tangent line must be horizontal This is important enough to state as a theorem though we will not prove it Theorem 5 1 1 Fermat s Theorem To find the maximum and minimum of a function you should first understand that these points known as extrema are where a function reaches its highest or lowest values In the realm of calculus I use various tools to determine these points which are crucial in analyzing the behavior of functions

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what is a minimum and maximum - Maxima and minima are the maximum or the minimum value of a function within the given set of ranges For the function under the entire range the maximum value of the function is known as the absolute maxima and the