For a function f that is continuous on the closed interval [1,5] with f(1)=−3 and f(5)=7, which of the following must be true?
a) There exists c∈(1,5) such that f(c)=10.
b) There exists c∈(1,5) such that f(c)=0.
c) The function takes only positive values on (1,5).
d) The function is differentiable on (1,5).