1, the derivative of the extreme point of differentiable function must be equal to 0.

But if there is no such word as "derivable", it would be wrong.

For example, the function f (x) = | x | (there are other functions that can give you examples).

X=0 is the extreme point, but the derivative of x=0 does not exist.

2. The point where the derivative is equal to 0 is not necessarily the extreme point.

For example, the function f(x)=sinx (there are other functions that can give you examples).

The derivative is equal to 0 when x=0, but it is not an extreme point when x=0.

To judge whether it is an extreme point, besides the derivative is equal to 0, it is also necessary to judge whether the left and right derivative values of the point are opposite.