Past exam of the mathematics course of the University of Oxford / 2021 / Prelims / Mathematics II / 4 / a / ii

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- Solution ii

Solution

The mean value theorem states: if a real-valued function

f

is continuous on a closed interval

[u, v]

, where

u < v

, and differentiable on

(u, v)

, then there is

c \in (u, v)

with

f (v) - f (u) = f^{'} (c) (v - u) .

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