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 ...

Find chapter notes of chapter Continuity and Differentiability including important topics like continuous functions, differentiable functions, chain rule, derivative of some functions, logarithmic ...

These notes are prepared by Subject Experts of Mathematics including all important topics related to chapter Continuity and Differentiability like continuous functions, sum, difference, product ...