The third derivative is not 0, and there are two cases.

1 and the third derivative is positive, indicating that the second derivative increases monotonically around this point.

So the second derivative on the left side of this point is negative, which means that the first derivative on the left side of this point is monotonically decreasing and convex upward.

The second derivative on the right is positive, indicating that the first derivative on the right of this point is monotonically increasing and concave downward.

So this point is an inflection point.

2. The third derivative is negative, which means that the second derivative decreases monotonously around this point.

So the second derivative on the left side of this point is positive, which means that the first derivative on the left side of this point is monotonically increasing and concave downward.

The second derivative on the right is negative, that is to say, the first derivative on the right of this point is monotonically decreasing and convex.

So this point is an inflection point.

So whether the third derivative is positive or negative, it is an inflection point.