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Rolle's theorem | mathematical analysis | elementary level
3 months ago
21
Science
mathematics
analysis
mathematical analysis
real analysis
calculus
derivative
differentiable
function
extremum
local extremum
Episode 78.
Rolle's theorem | mathematical analysis | elementary level.
Branch of mathematics: mathematical analysis.
Difficulty level: elementary.
Rolle's theorem. Suppose we have a function $f$ on the closed interval $[a,b]$. Suppose that it is continuous on the closed interval $[a,b]$ and differentiable on the open interval $(a,b)$. Suppose also that $f(a)=f(b)$. Then there exists an interior point $c \in (a,b)$ such that $f'(c)=0$.
Mathematical analysis. Calculus.
#MathematicalAnalysis #Calculus
The same video on YouTube:
https://youtu.be/PBHIsRNaN-Y
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