Suppose g is differentiable on the real line and satisfies g′(x)<0 for x<3 and g′(x)>0 for x>3. Which statement describes the behavior of g at x=3?
a) g has no local extremum at x=3 because g′ changes sign.
b) g has a point of inflection at x=3.
c) g has a local minimum at x=3.
d) g has a local maximum at x=3.