Let $(A,d)$ - dg-algebra with unit over field $k$ such that $H^i(A) = 0$ for $i > 1$, then $HH_i(A) = 0, i < -1$. I prove that using bar resolution, fact that cohomology commutes with filtered colimits and bicomplex spectral sequence. But I am new in homological algebra and not really sure that my proof is valid. So, that can be valid?
It maybe useful to notice that fact $H^i(A) = 0$ for $i > 0$ then $HH_i(A) = 0, i < 0$ is 100% true, it is classical result. So, "my" fact is slightly stronger version of it.