Saturday, November 22, 2008

Lagrange's Mean value theorem

When f(x) is a function defined on [a,b] such that

i) it is continuous on [a,b] and
ii) it is differentiable on (a,b)

there exists a real number c that belongs to (a,b) such that

f'(c) = (f(b)-f(a))/(b-a)

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