Question

f(x)=(x+2)^3-4. The point (-2, -4) is which of the following? A) An absolute maximum. B) An absolute minimum. C) A critical point but not an extremum. D) Not a critical point. E) None of these

Answer 1

option c is correct..a critical point but not an extremum. this is because if you differentiate f(x) once, and find f'(x) at that point, it turns out to be 0. but now if you double differentiate and find f"(x) at that point, it is still 0. so it is a crictical point but neither a maxima or a minima