A function g is twice differentiable and satisfies g′(x)>0 for x<2, g′(2)=0, and g′(x)>0 for x>2. In addition, g′′(2)=0 and g′′ changes sign at x=2. Which statement best describes the behavior of g at x=2?
a) g has a local maximum at x=2 because g′(2)=0 and g′′ changes sign.
b) g has neither a local maximum nor a local minimum but does have a point of inflection at x=2.},{
c) g has a local minimum at x=2 because g′′ changes sign from negative to positive.
d) No conclusion can be drawn since g′′(2)=0 provides insufficient information.