lesson 3.2 rolle and mean value theorems

2
Rolle’s Theorem a b 1. If f is continuous on [a,b], AND 2. Differentiable on (a,b), AND 3. f(a) = f(b), THEN… …you are guaranteed at least one value c on (a,b) where f’(c) = 0.

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Page 1: Lesson 3.2 Rolle and Mean Value Theorems

Rolle’s Theorem

a b

1. If f is continuous on [a,b], AND2. Differentiable on (a,b), AND 3. f(a) = f(b), THEN……you are guaranteed at least one value c on (a,b) where f’(c) = 0.

Page 2: Lesson 3.2 Rolle and Mean Value Theorems

Mean Value Theorem

a b

1. If f is continuous on [a,b] AND2. Differentiable on (a,b), THEN……there is at least one value c on (a,b) where ab

)a(f)b(f)c(f