Question

find the relative extrema: f(x)=x^3-27

Answer 1

f"(x) tells if the extremum at that point is a maximum or a minimum. If the sign is positive, the curve will slope upward, and the extremum is a minimum and vice versa

Answer 2

You should first find f'(x)

Answer 3

Then find f'(x), when x=0

Answer 4

Once you have the values, you will differentiate f'(x) once more, and get f''(x). From here substitute the values into f''(x) and you can find whether if its maximum or minimum