Rolle's theorem

Rarely Tested

If $$f$$ is continuous on $$[a,b]$$, differentiable on $$(a,b)$$, and $$f(a)=f(b)$$, then there exists $$c \in (a,b)$$ such that $$f'(c)=0$$.
Guarantees a point where the derivative is zero under given conditions.
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