A function is defined on the interval

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

Problem

A function

f

is defined on the interval

[2,7]

. Which of the following hypotheses is sufficient to guarantee that for every real number

d

satisfying

f(2)<d<f(7)

there exists

c\in(2,7)

such that

f(c)=d

? (a)

f

is differentiable on

(2,7)

but may have jump discontinuities at

x=2

and

x=7

. (b)

f

is continuous on

[2,7]

. (c)

f

is strictly increasing on

[2,7]

but not necessarily continuous. (d)

f

is continuous on

(2,7)

only.