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I have a homework Question to answer which is:

True or False: Between 2 sequential roots of $f'(x)$ there is at most one root for $f(x)$

I think this is true since $f(x)$ would be monotone unless $f'(x)$ is equal to $0$ on an interval - but in that case what are 2 sequential values of the roots?

Can someone help me with this question?

Thanks :)

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    Not true if it isn't differentiable at all values on the interval, even if continuous. But true if differentiable everywhere in the interval.2012-01-06

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