Let f be three times differentiable on R with f′(5)=0, f′′(5)=0, and f′′′(5)<0. Which of the following statements about x=5 is correct?
a) f has a local maximum at x=5.
b) f has a local minimum at x=5.
c) f has a point of inflection at x=5 and neither a local maximum nor a local minimum.
d) The information given is insufficient to classify the critical point at x=5.