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* Page found: Mittelwertsatz (eq math.1082.0)

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TeX (original user input): 

\begin{align}
  & \text{F }\!\!\ddot{\mathrm{u}}\!\!\text{ r jede stetig}\text{, differentierbare Funktion f(x):}\left[ {{\text{x}}_{\text{0}}}\text{,}{{\text{x}}_{\text{1}}} \right]\to \mathbb{R}:\exists \xi \in \left( {{\text{x}}_{\text{0}}}\text{,}{{\text{x}}_{\text{1}}} \right): \\ 
 & f\left( {{x}_{1}} \right)-f\left( {{x}_{0}} \right)=f'\left( \xi  \right)\left( {{x}_{1}}-{{x}_{0}} \right) \\ 
\end{align}

TeX (checked): 

{\begin{aligned}&{\text{F }}\!\!{\ddot {\mathrm {u} }}\!\!{\text{ r jede stetig}}{\text{, differentierbare Funktion f(x):}}\left[{{\text{x}}_{\text{0}}}{\text{,}}{{\text{x}}_{\text{1}}}\right]\to \mathbb {R} :\exists \xi \in \left({{\text{x}}_{\text{0}}}{\text{,}}{{\text{x}}_{\text{1}}}\right):\\&f\left({{x}_{1}}\right)-f\left({{x}_{0}}\right)=f'\left(\xi \right)\left({{x}_{1}}-{{x}_{0}}\right)\\\end{aligned}}

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F u¨ r jede stetig, differentierbare Funktion f(x):[x0,x1]→ℝ:∃ξ∈(x0,x1):f(x1)−f(x0)=f′(ξ)(x1−x0)
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mtext>F&#xA0;</mtext></mrow><mspace width="-0.167em"></mspace><mspace width="-0.167em"></mspace><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">u</mi></mrow><mo>¨</mo></mover></mrow></mrow><mspace width="-0.167em"></mspace><mspace width="-0.167em"></mspace><mrow data-mjx-texclass="ORD"><mtext>&#xA0;r jede stetig</mtext></mrow><mrow data-mjx-texclass="ORD"><mtext>, differentierbare Funktion f(x):</mtext></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msub><mrow data-mjx-texclass="ORD"><mtext>x</mtext></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mtext>0</mtext></mrow></mrow></msub><mrow data-mjx-texclass="ORD"><mtext>,</mtext></mrow><msub><mrow data-mjx-texclass="ORD"><mtext>x</mtext></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mtext>1</mtext></mrow></mrow></msub><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo accent="false">&#x2192;</mo><mrow data-mjx-texclass="ORD"><mi mathvariant="double-struck">&#x211D;</mi></mrow><mi>:</mi><mi mathvariant="normal">&#x2203;</mi><mi>&#x03BE;</mi><mo>&#x2208;</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mrow data-mjx-texclass="ORD"><mtext>x</mtext></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mtext>0</mtext></mrow></mrow></msub><mrow data-mjx-texclass="ORD"><mtext>,</mtext></mrow><msub><mrow data-mjx-texclass="ORD"><mtext>x</mtext></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mtext>1</mtext></mrow></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>:</mi></mtd></mtr><mtr><mtd></mtd><mtd><mi>f</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>&#x2212;</mo><mi>f</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><msup><mi>f</mi><mo>&#x2032;</mo></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>&#x03BE;</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>&#x2212;</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>

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Calculated based on the variables occurring on the entire Mittelwertsatz page

Identifiers

  • u¨
  • ℝ
  • ξ
  • f
  • x1
  • f
  • x0
  • f
  • ξ
  • x1
  • x0

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