Chapter 4.2

Theorems:

   Rolle’s Theorem: special case theorem.  Let f be a function that satisfies the following 3 hypotheses:

1. f is continuous on a closed interval [a,b]

2. f is differentiable on open interval (a,b)

3. f(a) = f(b)

                    Then there exists a number c in [a, b) such that f ‘(c) = 0

   Mean Value Theorem: 

1. f is continuous on a closed interval [a,b]

2. f is differentiable on open interval (a,b)

3. f(a) = f(b)

                    Then there exists a number c in [a, b] such that f ‘(c) =