By Team Aakash Byju's

Rolle’s Theorem Class 12 NCERT: Explained With Examples

In Class 12, Rolle's Theorem is a variant of the mean value theorem that satisfies certain conditions.

So, let us begin with learning the ‘Lagrange's Mean Value Theorem’ (LMVT).

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It states that: A function is defined on a closed interval [a,b] if it satisfies the below condition:

Note: Lagrange’s mean  value theorem is  also known as  ‘first mean value theorem’.

Now, let us see the special case of LMVT, that defines Rolle's Theorem.

The first conditions are the same for both LMVT and Rolle’s Theorem, but the third special condition for Rolle’s theorem is:

Mathematical statement of  Rolle's Theorem is

Example:

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