Stationary Points - point of inflextion and min and max I have the question "Find the coordinates of any stationary points on each curve and determine whether each stationary point is a maximum, minimum or point of inflection. Y = X^3 + 3X^2 + 3X" The solution for this question is: enter image description here I understand everything such as differentiating and finding the coordinates. However I do not understand why the coordinates (-1, -1) is point of inflexion. What is point of inflextion and how can you use the table above to find this or if the stationary point is max or min ?

We have a minimum, if the first derivate is $0$ and the second derivate is positive.

We have a maximum, if the first derivate is $0$ and the second derivate is negative.

We have an inflection point , if the second derivate is $0$ and the third derivate is non-zero.