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It has a face value of 5 but a local value of 5000
(local value)-(face value)=(7000-7)=6993
That refers to the highest and lowest value of a function. A "local maximum" (or local minimum) refers to a value that is higher than any near-by value, for a certain neighborhood.
Its face value is 6 but its numerical value in 586,723 is 6,000
An "extreme value" is either a local maximum, or a local minimum - i.e., a point which is greater than all the points in a certain neighborhood, or less than all points in a certain neighborhood.