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.

Intermediate value theorem facts for kids

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