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Darboux's theorem | mathematical analysis | intermediate level
1 year ago
2
Health & Science
mathematics
analysis
mathematical analysis
real analysis
calculus
derivative
differentiable
function
Rolle
Rolle's theorem
Episode 80.
Darboux's theorem | mathematical analysis | intermediate level.
Branch of mathematics: mathematical analysis.
Difficulty level: intermediate.
Darboux's theorem. Suppose we have a function $f$ on the closed interval $[a,b]$. Suppose that it is differentiable on the closed interval $[a,b]$. Then the derivative $f'$ has the intermediate value property: for any $y$ between $f'(a)$ and $f'(b)$, there exists a point $c$ such that $f'(c)=y$.
Mathematical analysis. Calculus.
#MathematicalAnalysis #Calculus
The same video on YouTube:
https://youtu.be/5W2Lzy_7tVg
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