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1.16 Working with the Intermediate Value Theorem (IVT)
#intermediatevaluetheorem
#ivt
⏱️ 1 min read
written by
anusha tekumulla
June 7, 2020
The Intermediate Value Theorem (IVT)
The intermediate value theorem focuses on a crucial part of continuity: for any function f(x) that's continuous over the interval [a, b], the function will take any y-value between f(a) and f(b) over the interval. 📈
Specifically, it means that for any value L between f(a) and f(b), there's a value c in [a,b] for which f(c) = L.
While this may sound confusing, it is actually very simple. As we have discussed before, continuous functions have to be drawn without lifting the pencil. If we know the graph passes through (a, f(a)) and (b, f(b)) then it must pass through any y-value between f(a) and f(b).
Image courtesy of Math is Fun
As you can see in the graph above, you can use the intermediate value theorem to prove that a function will cross a line at least once in an interval [a, b]. 👍
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