The correct answer to the question is Lagrange's Mean Value Theorem.

Lagrange's Mean Value Theorem (MVT) states that for a function that is continuous on a closed interval $[a, b]$ and differentiable on the open interval $(a, b)$, there exists at least one point $c$ in $(a, b)$ such that the derivative (slope of the tangent) at $c$ is equal to the average rate of change (slope of the secant line) between $a$ and $b$.

Would you like further details on how this theorem works or its applications?

Here are five related questions:

1. What is the geometric interpretation of the Mean Value Theorem?
2. How does Rolle's Theorem relate to the Mean Value Theorem?
3. Can the Mean Value Theorem be applied to non-differentiable functions?
4. What is the physical interpretation of the Mean Value Theorem in real-world contexts?
5. How do we prove Lagrange's Mean Value Theorem?

Tip: Always check if the function meets the conditions (continuity and differentiability) before applying the Mean Value Theorem.