It is known that if a differentiable function f has two equal values f(a)=f(b) , then there is a value f(c) between them which is a maximum or minimum for that interval. However, if the one sided derivatives at any x between a and b are not infinite, nor equal, what could be said about the one sided derivatives in c? Could it be said that it is greater or lower than 0?
2026-02-23 09:28:27.1771838907
Generalization of Rolle's Theorem
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