$\textbf{Mean value theorem}$
Let $a<b$ be real numbers and $f:[a,b]\to \R$ a continuous function on the closed interval $[a,b]$ and differentiable on the open interval $(a,b)$. Then there exists some $c$ in $(a,b)$ such that $$f^{\prime}(c)=\frac{f(b)-f(a)}{b-a}.$$
$\textbf{Mean value theorem}$
Let $a<b$ be real numbers and $f:[a,b]\to \R$ a continuous function on the closed interval $[a,b]$ and differentiable on the open interval $(a,b)$. Then there exists some $c$ in $(a,b)$ such that $$f^{\prime}(c)=\frac{f(b)-f(a)}{b-a}.$$
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๐๐๐๐งย ๐ฏ๐๐ฅ๐ฎ๐ย ๐ญ๐ก๐๐จ๐ซ๐๐ฆ
Let ๐<๐ be real numbers and ๐:[๐,๐]โโ a continuous function on the closed interval [๐,๐] and differentiable on the open interval (๐,๐). Then there exists some ๐ in (๐,๐) such that
๐โฒ(๐)=๐(๐)โ๐(๐) / ๐โ๐.