Find the number of inflection points of $(x-2)^6(x-3)^9$
If $f(x)$ has $n$ critical points then even $f(x+a)$ will also have $n$ critical points.
So we can simplify it to finding the number of inflection points of $(x)^6(x-1)^9$.
I have evaluated the double derivative to be:
Clearly, the double derivative is $0$ at $4$ points, $0$, $1$ and the roots of the quadratic. But curvature is not changing around $x=0$ so it's not an inflection point.
Thus, there should be $3$ inflection points.
But answer given is $1$ inflection point only.
Please let me know what concept am I missing on.
I tried my level best to zoom into the graph and catch three critical points but there appears to be only one.