What are the Three Conditions of Rolle's Theorem?

Rolle’s theorem is a special case of the mean-value theorem of differential calculus.

“All three conditions of Rolle’s theorem are important for the theorem to be true:

Condition 1: f(x) is continuous on the closed interval [a,b];

Condition 2: f(x) is differentiable on the open interval (a,b);

Condition 3: f(a)=f(b).”

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