Discussion on Application of Derivatives

 LAGRANGE’S MEAN VALUE THEOREM

This theorem is in fact the general version of Rolle’s theorem. It says that if  y = f(x) be a given function which is;
(i) Continuous in [a , b]
(ii) Differentiable in (a , b)

Then f'(x) = f(b)–f(a)/b–a. for a least once for some x ∈ (a, b)
Let A ≡ (a , f (a)) and B º (b , f (b)). Slope of Chord AB = f(b)–f(a)/b–a