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Intermediate value theorem facts for kids

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The intermediate value theorem says that if a function, f, is continuous over a closed interval [a,b], and is equal to f(a) and f(b) at either end of the interval, for any number, c, between f(a) and f(b), we can find an x so that f(x) = c.

This means that if a continuous function's sign changes in an interval, we can find a root of the function in that interval. For example, if f(1) = -1 and f(2) = 2, we can find an x in the interval [1,2] that is a root of this function, meaning that for this value of x, f(x)=0, if f is continuous. This corollary is called Bolzano's theorem.

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Intermediate value theorem Facts for Kids. Kiddle Encyclopedia.