Which of the following sets of hypotheses is sufficient to ensure that a real-valued function f attains the value d for some c in the interval [a,b]?
a) f is differentiable on (a,b), and d lies between f(a) and f(b).
b) f is strictly increasing on [a,b], and d lies between f(a) and f(b).
c) f is continuous on [a,b], and d lies between f(a) and f(b).
d) f is continuous on (a,b), and d lies between f(a) and f(b).