- #1

PFuser1232

- 479

- 20

__Mean Value Theorem__

Suppose that ##f## is a function that is continuous on ##[a,b]## and differentiable on ##(a,b)##. Then there is at least one ##c## in ##(a,b)## such that:

$$f'(c) = \frac{f(b) - f(a)}{b - a}$$

My question is: wouldn't it be better to state that ##c## is in ##[a,b]## rather than ##(a,b)##? For example, if ##f(x) = 2## for ##1 \leq x \leq 3##, then:

$$f'(x) = 0 = \frac{f(3) - f(1)}{2}$$

For all ##x##, including 3, which is one of the endpoints of the interval.