Question

g(x) is a differentiable function on the closed interval [a,b]. which of the following must be true?
a) for every x in [a,b], g(x) is between g(a) and g(b)
b) for every k between g(a) and g(b), there is a value c in [a,b] such that g(c)=k
c) there is at least one x in [a,b] such that g ' (x)=0
d) lim as x goes to infinity does not exist
e) g " (0) = 0

Answer 1

b, this is from the intermediate value theorem

Answer 2

this is because differentiability implies continuity