Let p(x)=x4. At x=0, one has p′(0)=0 and p′′(0)=0. Which of the following best describes the point x=0?
a) x=0 is neither a local maximum nor a local minimum because p′′(0)=0.
b) x=0 is a local maximum because p′(x) changes from positive to negative at x=0.
c) x=0 is a local minimum because p′(x) changes from negative to positive at x=0.
d) x=0 is an inflection point because p′′(0)=0."