Let $f(x)$ be a real-valued function all of whose derivatives exist. Recall that a point $x_0$ in the domain is called an inflection point of $f(x)$ if the second derivative $f^”(x) $ changes sign at $x_0$. Given the function $f(x)=\frac{x^5 }{20}-\frac{x^4 }{2}+ 3x+1$, which of the following statements are true?
- $x_0 =0$ is not an inflection point
- $x_0 =6$ is the only inflection point
- $x_0 =0$ and $x_0 =6$, both are inflection points
- The function does not have an inflection point
