Rolle's theorem | mathematical analysis | elementary level

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

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