Extreme value theorem
Continuous real function on a closed interval has a maximum and a minimum
Extreme value theorem
In real analysis, the extreme value theorem states that if a real-valued function f {\displaystyle f} is continuous on the closed and bounded interval [ a , b ] {\displaystyle [a,b]} , then f {\displaystyle f} must attain a maximum and a minimum, each at least once. That is, there exist numbers c {\displaystyle c} and d {\displaystyle d} in [ a , b ] {\displaystyle [a,b]} such that: f ( d ) ≤ f ( x ) ≤ f ( c ) ∀ x ∈ [ a , b ] . {\displaystyle f...
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