Which of the following sets of hypothesis guarantees that a real-valued function…

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

Problem

Which of the following sets of hypothesis guarantees that a real-valued function

f

defined on

[a,b]

has at least one real number

c

(a,b)

such that

f(c)=0

? (a)

f

is differentiable on

(a,b)

and

f(a)=f(b)=0

. (b)

f

is continuous on

[a,b]

and

f(a)

and

f(b)

have opposite signs. (c)

f

is differentiable on

(a,b)

and

f(a)

and

f(b)

have opposite signs. (d)

f

is continuous on

[a,b]

and

f(a)\,f(b)>0