Next question: You said that a function has a minimum or a maximum in some point x when its first derivative f'(x) =0 for this x.
Now look at a constant function, such as y=4. The derivative of this function is y'(x) = 0. But the function does not have a maximum or a minimum, it is totally flat. Can you explain this contradiction?
Answer A: It's not a contradiction. The fact that the first derivative is zero for some x, tells you that the tangent to the curve is horzontal for that x. That makes sense here, because, indeed, the tangent to the curve y=4 is horizontal for all x.
But in this case is the SECOND derivative also zero. You have a maximum or a minimum at some point x only when the first derivative f'(x) = 0 AND the second derivative f''(x) != 0.
Answer B: Well yes, this really looks like a contradiction -- I guess it means that everything we have learned is simply wrong!! Too bad