Absolute or Global maximum
the largest overall value of a function
The absolute or global maximum of a function refers to the largest value of the function over its entire domain. It is a single value that represents the maximum point of the function, and it is considered global because it represents the function’s highest point over the entire domain.
To find the absolute maximum of a function, you need to find all the critical points of the function, such as points where the derivative equals zero or points where the derivative does not exist. Then check the function’s value at these critical points and the endpoints of the domain to determine which point gives the largest value.
It is essential to note that not all functions have an absolute maximum. For example, if a function has an unbounded domain, the function may not have a highest point as the function continues to increase indefinitely.
In summary, the absolute or global maximum represents the largest value of a function over its entire domain, and it can be found by determining all critical points and endpoints of the domain and then evaluating them to determine which point gives the highest value.
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