I think this is a theorem, and I'm telling myself that I've proved it. Just a shout out for any possible counter-examples:(adsbygoogle = window.adsbygoogle || []).push({});

If a function f(x) is continuous on some interval and has non-zero derivatives at its root(s) (where f(x')=0 ) then there is some interval around the roots where there are no other roots, and f(x)><0 for x><x' as f'(x')><0.

It just says a function crossing the x-axis comes from below and goes above or comes from above and goes below when the derivative at the point is not zero. Any counter-examples?

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# Theorem on continuous function crossing x-axis

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