A function f is defined on the interval [2,7]. Which of the following hypotheses is sufficient to guarantee that for every real number d satisfying f(2)<d<f(7) there exists c∈(2,7) such that f(c)=d?
a) f is differentiable on (2,7) but may have jump discontinuities at x=2 and x=7.
b) f is continuous on [2,7].
c) f is strictly increasing on [2,7] but not necessarily continuous.
d) f is continuous on (2,7) only.