Mathematics

Problem

For a function that is continuous on

[a,b]

and differentiable on

(a,b)

, which statement is always true? a)

\displaystyle f'(x)=\frac{f(b)-f(a)}{b-a}\text{ for every }x\in(a,b)

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

\displaystyle \text{There exists }c\in(a,b)\text{ such that }f'(c)=\frac{f(b)-f(a)}{b-a}

\displaystyle \text{There exists }c\in[a,b]\text{ such that }f'(c)=\frac{f(b)-f(a)}{b-a}