Which of the following statements best expresses the Intermediate Value Theorem (IVT)?

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Which of the following statements best expresses the Intermediate Value Theorem (IVT)? (a) If

f

is continuous on

[a,b]

and

d

is any number between

f(a)

and

f(b)

, then there exists

c

[a,b]

such that

f(c)=d

. (b) If

f

is continuous on

[a,b]

and

d

is any number between

f(a)

and

f(b)

, then there exists

c

(a,b)

such that

f(c)=d

. (c) If

f

is differentiable on

(a,b)

, then for any number

d

between

f(a)

and

f(b)

, there exists

c

(a,b)

such that

f(c)=d

. (d) If

f

is continuous on

[a,b]

, then there exists

c

(a,b)

such that

f(c)=\dfrac{f(a)+f(b)}{2}