Let f(x)=x4−4x3. Which statement about the critical points of f is correct?
a) x=0 is a local maximum, and x=3 is a local minimum
b) x=0 is a critical point that is not a local extremum, whereas x=3 is a local minimum
c) x=0 is not a critical point, while x=3 is a local minimum
d) Neither x=0 nor x=3 is a critical point because f′′(x) exists at both points