1. Rolle’s Theorem
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.
a
b

2. Mean Value Theorem
1. If f is continuous on [a,b] AND
2. Differentiable on (a,b), THEN…
f ( b) − f ( a )
…there is at least one value c on (a,b) where f ′( c ) =
b−a
a
b