Properties of Continuous Functions
- Intermediate Value Theorem
- It’s similar to the 625d10de79e1130000986347, so it’s kind of obvious.
- Should we recognize the existence of this theorem? (blu3mo)
- It’s similar to the 625d10de79e1130000986347, so it’s kind of obvious.
- Maximum Value Theorem
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A continuous function defined on a non-empty bounded closed interval has a maximum value and a minimum value.
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- It seems important to understand when these theorems do not hold true (blu3mo)(blu3mo)
- ① non-empty ② bounded ③ closed interval as the domain ④ continuous function
- In other words, if the domain is (-∞, ∞), there is no minimum or maximum value (since it is not bounded).
- If the domain is (-1, 1), there is no minimum or maximum value (since it is an open interval).
- However, it doesn’t mean that they absolutely don’t have minimum or maximum values.
- Even if it’s not a closed interval, quadratic functions, for example, have minimum or maximum values.