Continuity and Differentiability

Mean Value Theorem


  • Rolle's Theorem: If f : [a, b] → R is continuous on [a, b] and differentiable on (a, b) such that f(a) = f(b), then there exists some c in (a, b) such that f'(c) = 0.
  • Mean Value Theorem : If ƒ : [a, b] → R is continuous on [a, b] and differentiable on (a, b). Then there exists some c in (a, b) such that

             f'(c) = \frac{f(b)-f(a)}{b-a}

Part1: View the Topic in this video From 42:08 To 51:53

Part2: View the Topic in this video From 01:00 To 50:23

Part3: View the Topic in this video From 00:40 To 15:52

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1. Mean Value Theorem : If ƒ : [a, b] → R is continuous on [a, b] and differentiable on (a, b). Then there exists some c in (a, b) such that

         f'(c) = \frac{f(b)-f(a)}{b-a}