Finding Concavity in Curves

Suppose $$\frac{d^2y}{dx^2} = \frac{e^{-t}}{1-e^t}.$$

After locating the 2nd by-product, just how do I locate concavity? It is a lot easier to address for $t$ in a trouble like $t(2-t) = 0$, yet in this instance, addressing for $t$ appears harder. Does it have something to do with $e$? $e$ never ever comes to be $0$, yet at what factor is the contour upwards or downward?