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Intermediate value theorem - Wikipedia
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A converse of the mean value theorem made easy
4.4 The Mean Value Theorem | Calculus Volume 1
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A CONSTRUCTIVE CONVERSE OF THE MEAN VALUE THEOREM.
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Does the converse of Rolle's Theorem hold true? Let [math]f[/math] be continuous on [math][a,b][/math] and differentiable on [math](a,b)[/math]. If there exists [math]c[/math] in [math](a,b)[/math] such that [math]f'(c)=0[/math], does it follow that ...
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Mean Value Theorem - YouTube
Intermediate value theorem - Wikipedia
Does the converse of Rolle's Theorem hold true? Let [math]f[/math] be continuous on [math][a,b][/math] and differentiable on [math](a,b)[/math]. If there exists [math]c[/math] in [math](a,b)[/math] such that [math]f'(c)=0[/math], does it follow that ...