Mathematics

Problem

Let

f

be a differentiable function on the open interval

(a, b)

. I.

f

is continuous on the closed interval

[a, b]

. II.

f

is bounded on the open interval

(a, b)

. III. If

a < a_1 < b_1 < b

and

f(a_1) < 0 < f(b_1)

, then there exists number

c

such that

a_1 < c < b_1

and

f(c) = 0

. Which of the above statements must be true? a. Only I and II b. Only I and III c. Only II and III d. Only III