Math — Mean Value & Rolle's Theorem
MVT, Rolle's theorem and the mean value of an integral.
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f'(c) = \frac{f(b) - f(a)}{b - a}
\text{Rolle: } f(a)=f(b) \Rightarrow f'(c)=0
\bar{f} = \frac{1}{b-a}\int_a^b f(x)\,dx
c \in (a,b)