Recover a rational-curve parameter from an inflection
The curve has an inflection at the prescribed x-coordinate. Recover B, then find the ordinate, tangent coefficients and third derivative at that point. Work on the original domain. An excluded pole is never an inflection
\[u=x-(-3),\quad f(x)=u+\frac{-6}u+\frac B{u^2},\quad x\ne-3,\quad x_0=0\]
Use the tangent form y=mx+q. Report all five values exactly as integers or fractions; justify the concavity change in your written working