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# Intermediate Value Theorem

Course Topic(s): One-Variable Calculus | Theoretical Issues

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.

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 Current rating: 2.9 number of votes: 312 1 2 3 4 5

Subject classification(s): Continuity | Single Variable Calculus | Calculus

Creator(s): Izidor Hafner

Contributor(s): Wolfram Demonstrations Project

This resource was cataloged by Philip Yasskin

Publisher:
Wolfram Demonstrations Project

This review was published on March 13, 2011