By the Mean value Theorem there is c ∈(0,T) c ∈ (0, T) such that F ′(c)= F (T)−F (0) T −0 = 0. F ′ (c) = F (T) − F (0) T − 0 = 0. It follows that f′(c)= g′(c) f ′ (c) = g ′ (c) which is the same as to ...

The mean value theorem of calculus states that, given a differentiable function f on an interval [a, b], there exists at least one mean value abscissa c such that the slope of the tangent line at (c, ...

In a similar spirit to the probabilistic generalization of Taylor's theorem by Massey and Whitt [13], we give a probabilistic analogue of the mean value theorem. The latter is shown to be useful in ...