Why say "the extreme point does not necessarily make the derivative zero?"

Why say "the extreme point does not necessarily make the derivative zero?"

For example, when x0, y = - x, 0 is the extreme point, but there is no derivative

If derivative has extremum, is derivative necessarily 0

1. Derivative is a guiding function. It's a new function. If the new function has extreme value, it's the derivative function
The extreme value has its own derivative
2. It is not true to say in general: "derivative has extremum, derivative must be 0"
It should be said: "derivative function has extreme value, derivative function at its extreme point must be."

The second power of (- A's power) divided by the third power of (- A's power)

((-a)^3)^2/((-a)^2)^3=(a^6)/(a^6)=1