Rolle's Theorem

What are the state of Rolle's theorem?

Rolle's theorem

In calculus, Rolle's theorem essentially states that any real-valued differentiable function that attains equal values at two distinct points must have at least one stationary point somewhere between them—that is, a point where the first derivative (the slope of the tangent line to the graph of the function) is zero.

Definition Of Rolle's Theorem:-

Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that
 f(a) = f(b), then f′(x) = 0 for some x with a ≤ x ≤ b.


How do you determine if Rolle's theorem can be applied?

Understand and use the Mean Value Theorem. then there is at least one number c in (a , b ) such that f'(c)=0 . 2) there must be at least one point between a and b at which the derivative is 0 Page 3 AP Calc 3 Example: Determine whether Rolle's Theorem can be applied to f on the closed interval [a , b ].