Darboux's theorem | mathematical analysis | intermediate level

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

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