differentiability
posted by matthew .
If g is a differentiable function such that g(x) is less than 0 for all real numbers x and if f prime of x equals (x24)*g(x), which of the following is true? A. f has a relative maximum at x=2 and a relative minimum at x=2, B. f has a relative minimum at x=2 and a relative maximum at x=2, C. f has a relative minima at x=2 and at x=2, D. f has a relative maxima at x=2 and at x=2, E. It cannot be determined if f has any relative extrema.

The answer is B. f' changes from negative to positive at x = 2 and positive to negative at x = 2.