A differentiable function p is continuous on [1,7] and satisfies p′(4)=0 with p′(x)=0 for x=4. In addition, p′′(4)<0. Which statement about p at x=4 is most accurate?
a) p(4) is a relative minimum of p on [1,7].
b) p(4) is a relative maximum but need not be the absolute maximum on [1,7].
c) p(4) is both a relative maximum and the absolute maximum of p on [1,7].
d) x=4 is an inflection point of p on [1,7].