For a function that is continuous on the closed interval with and

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

Problem

For a function

f

that is continuous on the closed interval

[1,5]

with

f(1)=-3

and

f(5)=7

, which of the following must be true? (a) There exists

c\in(1,5)

such that

f(c)=10

. (b) There exists

c\in(1,5)

such that

f(c)=0

. (c) The function takes only positive values on

(1,5)

. (d) The function is differentiable on

(1,5)