# Mean Value Theorem

If a function is:

Continuous on [a, b].

Differentiable on (a, b).

Then, there exists a point, c (a, b) such that:

The geometric interpretation of the **Mean Value Theorem** tells us that there is a point where the tangent is parallel to the secant.

Rolle's Theorem is a special case of the **Mean Value Theorem**, in that **f(a) = f(b)**.

#### Example

Can the **Mean Value Theorem** be applied to f(x) = x³ on [−1, 2]?

The function f(x) is continuous on [−1, 2] and differentiable on (−1, 2) so the **Mean Value Theorem** can be applied:

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