(calculator not allowed)
Let g be a continuous function on the closed interval [0, 1]. Let g(0) = 1 and g(1) = 0.
Which of the following is NOT necessarily true?
(A) There exists a number h in [0, 1] such that g(h) ≥ g(x) for all x in [0, 1].
(B) For all a and b in [0, 1], if a = b, then g(a) = g(b).
(C) There exists a number h in [0, 1] such that g(h) == /
(D) There exists a number h in [0, 1] such that g(h):
(E) For all h in the open interval (0, 1), lim g(x) = g(h).
3
2
