Functions h and p are continuous on [a,b] and differentiable on (a,b). Suppose h′(x)>p′(x) for every x in (a,b). Which statement is necessarily true?
a) h and p intersect at least twice on (a,b).
b) h(x)−p(x) has a critical point in (a,b).
c) If h(a)=p(a), then h(x)>p(x) for all x∈(a,b].
d) There exists c∈(a,b) such that h′(c)=p′(c).