Is it an inflection point if the second derivative is a double root?
For example, would the function $f''(x)=x^2(x-3)(x-6)$ have 3 inflection points or 2?
Although it is clear that 3 and 6 are inflection points, would 0 be a point of inflection or a bounce?
[Math] Is it an inflection point if the second derivative is a double root
calculus
Best Answer
When we are unsure, we should refer to the definitions.
An inflection point is a point where the curvature changes its sign while a tangent exists. In this case, the curvature doesn't change sign at $0$, hence it is not an inflection point.