The object of this paper is to give a generalisation to vector valued functions of the classical mean value theorem of differential calculus. In that theorem we have for some c in the open interval a , b when f is a real valued function which is continuous on the closed interval a , b and differentiable on the open interval. The counterpart to (1) when f has values in an n -dimensional vector space turns out to be where c k a , b , 0 k , and .
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Robert McLeod (1965) studied this question.