We are given our function as
![y=\frac{-3}{x+4}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-3%7D%7Bx%2B4%7D)
For finding concavity , firstly we will find second derivative
![=-3\frac{d}{dx}\left(\frac{1}{x+4}\right)](https://tex.z-dn.net/?f=%3D-3%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%28%5Cfrac%7B1%7D%7Bx%2B4%7D%5Cright%29)
![=-3\left(-\frac{1}{\left(x+4\right)^2}\right)\cdot \:1](https://tex.z-dn.net/?f=%3D-3%5Cleft%28-%5Cfrac%7B1%7D%7B%5Cleft%28x%2B4%5Cright%29%5E2%7D%5Cright%29%5Ccdot%20%5C%3A1)
![y'=\frac{3}{\left(x+4\right)^2}](https://tex.z-dn.net/?f=y%27%3D%5Cfrac%7B3%7D%7B%5Cleft%28x%2B4%5Cright%29%5E2%7D)
now, we can find derivative again
![y''=\frac{d}{dx}\left(\frac{3}{\left(x+4\right)^2}\right)](https://tex.z-dn.net/?f=y%27%27%3D%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%28%5Cfrac%7B3%7D%7B%5Cleft%28x%2B4%5Cright%29%5E2%7D%5Cright%29)
![=3\frac{d}{dx}\left(\left(x+4\right)^{-2}\right)](https://tex.z-dn.net/?f=%3D3%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%28%5Cleft%28x%2B4%5Cright%29%5E%7B-2%7D%5Cright%29)
![y''=3\left(-\frac{2}{\left(x+4\right)^3}\right)\cdot \:1](https://tex.z-dn.net/?f=y%27%27%3D3%5Cleft%28-%5Cfrac%7B2%7D%7B%5Cleft%28x%2B4%5Cright%29%5E3%7D%5Cright%29%5Ccdot%20%5C%3A1)
![y''=-\frac{6}{\left(x+4\right)^3}](https://tex.z-dn.net/?f=y%27%27%3D-%5Cfrac%7B6%7D%7B%5Cleft%28x%2B4%5Cright%29%5E3%7D)
now, we can know second derivative is undefined when denominator =0
so, we set denominator =0
and then we can solve for x
![x+4=0](https://tex.z-dn.net/?f=x%2B4%3D0)
![x=-4](https://tex.z-dn.net/?f=x%3D-4)
now, we can draw a number line and locate x=-4
and then we can find sign of second derivative on each intervals
so,
Concave downward interval:
![(-4,\infty)](https://tex.z-dn.net/?f=%28-4%2C%5Cinfty%29)