For a function defined on the closed interval

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

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)