Which set of hypotheses is sufficient to guarantee that a real-valued function has…

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

Problem

Which set of hypotheses is sufficient to guarantee that a real-valued function

f

has some

c

(a,b)

for which

f(c)=0

? (a)

f

is continuous on

(a,b)

and

f(a)f(b)<0

. (b)

f

is continuous on

[a,b]

and

f(a)=f(b)

. (c)

f

is continuous on

[a,b]

and

f(a)f(b)<0

. (d)

f

is continuous on

[a,b]

and

f(a)f(b)>0