Which of the following sets of hypotheses is sufficient to ensure that a real-valued…

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

Problem

Which of the following sets of hypotheses is sufficient to ensure that a real-valued function

f

attains the value

d

for some

c

in the interval

[a,b]

? (a)

f

is differentiable on

(a,b)

, and

d

lies between

f(a)

and

f(b)

. (b)

f

is strictly increasing on

[a,b]

, and

d

lies between

f(a)

and

f(b)

. (c)

f

is continuous on

[a,b]

, and

d

lies between

f(a)

and

f(b)

. (d)

f

is continuous on

(a,b)

, and

d

lies between

f(a)

and

f(b)