The function f has a continuous second derivative, and it satisfies f(1)=−4,f ′ (1)=0 and f (1)=0. We can conclude that
A. f has neither a local maximum nor a local minimum at 1
B. f has a local maximum at 1
C. f has a local minimum at 1
D. We cannot determine if A, B, or C hold without more information.