In this video I explain what the Rolle's Theorem is and show several examples illustrating it and also how you can use it to determine the number of roots in an equation.

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Rolle’s Theorem

Used in proving the Mean Value Theorem

Example 1

Example 2

Solution:

Rolle's Theorem is an "Existence" Theorem

An existence theorem says a number with some conditions exists but doesn't say how to get that number.

In other words, Rolle's Theorem states that a number exists in which the derivative is 0 but doesn't state what that number is.