Rolle’s theorem  Derivative Applications
Rolle’s theorem
Basic concepts:
 Definition of derivative
 Critical number & maximum and minimum values
Lessons
Notes:
Let $f(x)$ satisfy the three following conditions:
1) $f(x)$ is continuous on the interval $[a, b]$
2) $f(x)$ is differentiable on the interval $(a, b)$
3) $f(a) = f(b)$
If the conditions are fulfilled, then Rolle’s Theorem states that there must be a number (call it $c$) such that $a < c < b$ and $f'(c) = 0$.

1.
Rolle’s Theorem Overview