For a twice differentiable function f, suppose f′(c)=0 and f′′(c)=0. Which one of the following statements correctly describes x=c?
a) x=c is definitely a point of inflection of f.
b) x=c is a local extremum; the nature can be decided from the sign of f′′′(c).
c) The second derivative test is inconclusive and the sign change of f′(x) around c must be examined.
d) x=c is definitely a local minimum of f.