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If $$f$$ is continuous on [a,b], differentiable on (a,b), and $$f(a) = f(b)$$, then:
$$\exists \, c \in (a,b) \quad \mathrm{such that} \quad f'(c) = 0$$
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If $$f$$ is continuous on [a,b], differentiable on (a,b), and $$f(a) = f(b)$$, then:
$$\exists \, c \in (a,b) \quad \mathrm{such that} \quad f'(c) = 0$$
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