## 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 thatf'(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}