A twice-differentiable function g satisfies g′(4)=0 and g′′(4)<0. Which statement best describes the behavior of g at x=4?
a) g has a local minimum at x=4 (the graph is concave up).
b) g has a local maximum at x=4 (the graph is concave down).
c) g has a point of inflection at x=4 (the concavity changes).
d) The given information is insufficient to determine the local behavior at x=4 (more analysis is needed).