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)
How to make this a box plot 16,16,16,20,21,21,23,25,26,26,28,28
GREYUIT [131]
Answer:
16x3 (repeats 3 times) 20x1 21x2 23x1 25x1 26x2 28x2
Step-by-step explanation:
30 min: 60min-30min= 30 min and 30 min is half an hour. So since 30 min is half an hour you divide 4 by 2 and get 2 miles.
45 min: 60min-45min= 15 min. 15 is one quarter of an hour so, since you are going 4mph. So you do 4mph divided by another for because there are four quarters in one hour, which gives you one mile. Then you 1 mile 3 times because 15+15+15=45. So the answer is 3 miles.
2 hours: 2x4= 8 miles
3 hours: 3 hours x 4mph= 12 miles
answer:
ii- 7
iii- 5
Step-by-step explanation:
sorry if its wrong im not for sure
Answer:
I think the answer is 6 cause if you do 54+6=60