Lagrange's mean value theorem:

This theorem is the general version of Rolle 's Theorem. It says that if y = f(x);

(i)         Continuous in [a , b]           

(ii)        Differentiable in (a , b)

Then .

Let A ≡ (a , f (a)) and B ≡ (b , f (b)). The slope of Chord 

Illustration:   If a, b, are 2 numbers with a < b, show that a real number c can be found between a and b such that 3c² = b² + ab + a².

Solution:             Consider the function f(x) = x³ 

                              It is continuous and differentiable in (a, b).

                              Thus by LMVT, there exist a point c such that a < c < b and                 

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