Which set of hypotheses is sufficient to guarantee that a real-valued function f has some c in (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.