Suppose f is differentiable for all real numbers and satisfies f′(2)=0 and f′′(2)=0. A sign chart for f′ shows f′(x)<0 when x<2 and f′(x)>0 when x>2. Which of the following best describes the point x=2?
a) x=2 is a point of inflection of f.
b) x=2 is a local maximum of f.
c) x=2 is a local minimum of f.
d) No conclusion about extrema can be drawn from the given information.