**Rolle’s Theorem:**

If a function \( f(x) \) satisfies the following three conditions on a closed interval \([a, b]\):  
1. **Continuity**: \( f(x) \) is continuous on the closed interval \([a, b]\).  
2. **Differentiability**: \( f(x) \) is differentiable on the open interval \((a, b)\).  
3. **Equal Values at Endpoints**: \( f(a) = f(b) \).  

Then, there exists at least one \( c \in (a, b) \) such that:  
\[
f'(c) = 0
\]  

This means the function has at least one point where the slope of the tangent is zero (a horizontal tangent) within the interval.

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### Related Questions:
1. What is the geometrical interpretation of Rolle’s Theorem?
2. Can Rolle’s Theorem apply to a function that is not differentiable everywhere?
3. How does Rolle’s Theorem relate to the Mean Value Theorem?
4. Provide an example function that satisfies Rolle’s Theorem on a given interval.
5. How can one verify if a function meets the conditions of Rolle’s Theorem?

### Tip:
Always ensure to check both continuity and differentiability conditions before applying Rolle’s Theorem; they are key to its validity.

Explore Rolle's Theorem, which states that for a continuous and differentiable function on a closed interval with equal values at the endpoints, there exists at least one point where the derivative equals zero. Learn the conditions and application of this important theorem in calculus.

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