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WikiCards · Card list · Science cards · Extreme value theorem
Uncommon card · Science
Extreme value theorem, an Uncommon card
In real analysis, the extreme value theorem states that if a real-valued function f is continuous on the closed and bounded interval [ a, b ], then f must attain a maximum and a minimum, each at least once.
- Rarity
- Uncommon
- Domain
- Science
- ATK
- 66
- DEF
- 31
- Power
- 97
- Wikipedia reads a year
- 48,000
Power 97 (ATK + DEF): stronger than 40 % of WikiCards cards.
Extreme value theorem quiz: 3 questions
Three questions on the Extreme value theorem card, the way WikiCards duels ask them. Pick an answer, the facts are just below.
Which of these cards hits hardest (highest ATK)?
Answer
Extreme value theorem. Extreme value theorem 66 · Circumference 56 · Blue hour 51 · Fordite 48 ATK in WikiCards.
Which of these Wikipedia articles is read the most in a year?
Answer
Circumference. Circumference 120,000 · Blue hour 83,000 · Extreme value theorem 48,000 · Electrical cable 37,000 Wikipedia reads over a year.
In a duel, each round asks a question like these about the opposing card, with 15 seconds to answer.
The facts on the card
The card carries these facts from its Wikipedia article.
- That is, there exist numbers c and d in [ a, b ] such that: f ≤ f ≤ f ∀ x ∈ [ a, b ]. The extreme value theorem is more specific than the related boundedness theorem, which states merely that a continuous function f on the closed interval [ a, b ] is bounded on that interval, that is, there exist real numbers m and M such that: m ≤ f ≤ M ∀ x ∈ [ a, b ].
- The extreme value theorem is used to prove Rolle's theorem.
- In a formulation due to Karl Weierstrass, this theorem states that a continuous function from a non-empty compact space to a subset of the real numbers attains a maximum and a minimum.
Why it is Uncommon
Rarity in WikiCards follows a year of Wikipedia page views: the most read articles become Epic and Legendary cards. The Extreme value theorem article was read about 48,000 times in a year. ATK comes from the length of the article and DEF from its quality, so this card hits with 66 and blocks with 31: each hit it takes is cut by 12 %.
How to get Extreme value theorem
Open packs. Each pack holds five cards drawn from real Wikipedia articles, the rarest last, and the fifth card is always Rare or better. The odds are shown in the game. A free pack arrives every hour and two can wait, and the Coins you win in duels buy more packs.
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Credits
Text : Wikipedia, Extreme value theorem (revision), CC BY-SA 4.0. Photo : -- p b r ok s 1 3 talk?, Public domain, Wikimedia Commons.
