Question

If g is a differentiable function such that g(x) < 0 for all real numbers, x, and if f'(x) = (x^(2)-9)g(x), how do you know f has a min x=3 and a max at x=3

Answer 1

You can't have a minimum and a maximum at the same point... Do you mean the minimum value of f is at x=3 or that the value itself is 3?

Answer 2

**unless you consider constant functions, but even then I think the definitions of max/min aren't ambiguous.