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 in (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.