Intermediate value property: Difference between revisions
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==Definition== | ==Definition== | ||
A function <math>f</math> is said to satisfy the '''intermediate value property''' if, for every <math>a < b</math> in the domain of <math>f</math>, and every choice of real number <math>t</math> between <math>f(a)</math> and <math>f(b)/math>, there exists <math>c \in [a,b]</math> that is in the domain of <math>f</math> such that <math>f(c) = t</math>. | A function <math>f</math> is said to satisfy the '''intermediate value property''' if, for every <math>a < b</math> in the domain of <math>f</math>, and every choice of real number <math>t</math> between <math>f(a)</math> and <math>f(b)</math>, there exists <math>c \in [a,b]</math> that is in the domain of <math>f</math> such that <math>f(c) = t</math>. | ||
==Facts== | ==Facts== | ||
Latest revision as of 11:31, 7 September 2011
Definition
A function is said to satisfy the intermediate value property if, for every in the domain of , and every choice of real number between and , there exists that is in the domain of such that .
![{\displaystyle c\in [a,b]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/997256364b06acf0710e5d24da39e8c42991a249)
Facts
- Intermediate value theorem: This states that a continuous function on a closed interval satisfies the intermediate value property.
- Derivative of differentiable function on interval satisfies intermediate value property