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