(a) Assume that g and h are continuous on [a, b]. Use Corollary 2 to show that if g(a) < h(a) and h(b) < g(b), then there exists c ∈ [a, b] such that g(c) = h(c).

(b) Interpret the result of (a) in terms of the graphs of g and h, and show, by a graphical example, that the conclusion in (a) need not hold if one of g or h is not continuous.