extreme value theorem
[extreme value theorem|extreme value theorem] is a theorem in mathematical analysis that states any continuous function on a closed and bounded interval attains its maximum and minimum values.
Definition
extreme value theorem is a theorem in mathematical analysis that states any continuous function on a closed and bounded interval attains its maximum and minimum values. The theorem requires the function to be continuous on a closed bounded interval to guarantee the existence of these extrema.
Mechanism
extreme value theorem applies to continuous functions over closed, bounded intervals, ensuring they attain both absolute maximum and minimum values within that interval.
Comparison
extreme value theorem The extreme value theorem guarantees attainment of maximum and minimum on [a, b], whereas non-constant functions have averages strictly smaller than maximum and larger than minimum.