Mathematics | Lagrange’s Mean Value Theorem

Suppose f(x) be a function satisfying three conditions:

1) f(x) is continuous in the closed interval a <= x <= b

2) f(x) is differentiable in the open interval a < x < b

 

Then according to Lagrange’s Theorem, there exists at least one point ‘c’ in the open interval (a, b) such that:



f ‘ (c) = [f(a) – f(b) ] / (b – a)

 

We can visualize Lagrange’s Theorem by the following figure

f3

 

In simple words, Lagrange’s theorem says that if there is a path between two points A(a, f(a)) and B(b, f(a)) in a 2-D plain then there will be at least one point ‘c’ on the path such that the slope of the tangent at point ‘c’, i.e., (f ‘ (c)) is equal to the average slope of the path, i.e., f ‘ (c) = [f(a) – f(b) ] / (b – a)

 

This article has been contributed by Saurabh Sharma.
 
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