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Intermediate Value Theorem

Students get to adjust the second segment of a piecewise linear function on an interval \([a,b]\) to make it continuous or not. And they get to choose a value of \(c\) between \(f(a)\) and \(f(b)\). The graph then shows them a value of \(x\) for which \(f(x)=c\), as guaranteed by the Intermediate Value Theorem. Unfortunately, it gives a value of \(x\) even if the function is discontinuous as long as \(c\) is not within the jump discontinuity even though this is not guaranteed by the theorem. Perhaps a warning should appear saying the \(x\) occurs by luck even though it is not guaranteed by the theorem.
Average: 3 (329 votes)
Izidor Hafner
Philip Yasskin
Wolfram Demonstrations Project
Wolfram Demonstrations Project