Suppose f(x) is a polynomial with critical points at x=-1, x=2, and x=6. Assume that f''(x)=-3x^2+14x-4. Based on this information, which of the following statements is true about f(x)?

A. f(x) has a local maximum at x=-1.
B. f(x) has a local maximum at x=2.
C. f(x) has a local maximum at x=6.
D. There is not enough information to determine the location of the local maximum.