The function h(x)=x5−5x3 has a critical number at x=0. Which statement best describes this point?
a) x=0 is a local maximum because h′(x) changes from positive to negative at that point.
b) x=0 is a local minimum because h′′(0)>0.
c) x=0 is a point of inflection because h′′(0)=0 and h′ does not change sign there.
d) The nature of x=0 cannot be determined without evaluating higher–order derivatives such as h(4)(0).