Mathematics

Problem

For a function

f

defined on the closed interval

[a,b]

, which set of conditions is sufficient to guarantee at least one point

c\in(a,b)

satisfying

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

? a) Continuous on

(a,b)

only b) Differentiable on

(a,b)

only c) Continuous on

[a,b]

and differentiable on

(a,b)

d) Differentiable on

[a,b]

and continuous on

(a,b)