Step-by-step explanation:
Take the first derivative
![\frac{d}{dx} ( {x}^{3} - 3x)](https://tex.z-dn.net/?f=%20%5Cfrac%7Bd%7D%7Bdx%7D%20%28%20%7Bx%7D%5E%7B3%7D%20%20-%203x%29)
![3 {x}^{2} - 3](https://tex.z-dn.net/?f=3%20%7Bx%7D%5E%7B2%7D%20%20-%203)
Set the derivative equal to 0.
![3 {x}^{2} - 3 = 0](https://tex.z-dn.net/?f=3%20%7Bx%7D%5E%7B2%7D%20%20-%203%20%3D%200)
![3 {x}^{2} = 3](https://tex.z-dn.net/?f=3%20%7Bx%7D%5E%7B2%7D%20%20%3D%203)
![{x}^{2} = 1](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%3D%201)
![x = 1](https://tex.z-dn.net/?f=x%20%3D%201)
or
![x = - 1](https://tex.z-dn.net/?f=x%20%3D%20%20-%201)
For any number less than -1, the derivative function will have a Positve number thus a Positve slope for f(x).
For any number, between -1 and 1, the derivative slope will have a negative , thus a negative slope.
Since we are going to Positve to negative slope, we have a local max at x=-1
Plug in -1 for x into the original function
![( - 1) {}^{3} - 3( - 1) = 2](https://tex.z-dn.net/?f=%28%20-%201%29%20%7B%7D%5E%7B3%7D%20%20-%203%28%20%20-%201%29%20%3D%202%20)
So the local max is 2 and occurs at x=-1,
For any number greater than 1, we have a Positve number for the derivative function we have a Positve slope.
Since we are going to decreasing to increasing, we have minimum at x=1,
Plug in 1 for x into original function
![{1}^{3} - 3(1)](https://tex.z-dn.net/?f=%7B1%7D%5E%7B3%7D%20%20%20-%203%281%29)
![1 - 3 = - 2](https://tex.z-dn.net/?f=1%20-%203%20%3D%20%20-%202)
So the local min occurs at -2, at x=1
Given two points
, the slope of the line passing through the two points is
![m = \dfrac{A_y-B_y}{A_x-B_x}](https://tex.z-dn.net/?f=%20m%20%3D%20%5Cdfrac%7BA_y-B_y%7D%7BA_x-B_x%7D%20)
So, in your case, you have
![m = \dfrac{3-5}{-2-4} = \dfrac{-2}{-6} = \dfrac{1}{3}](https://tex.z-dn.net/?f=%20m%20%3D%20%5Cdfrac%7B3-5%7D%7B-2-4%7D%20%3D%20%5Cdfrac%7B-2%7D%7B-6%7D%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%20)
If Simone has 20 bills, then:
1/5 of 20 = 4 [hundreds]
1/4 of 20 = 5 [fifites]
1/10 of 20 = 2 [$20s]
4 * 100 + 5 * 50 + 2 * 20 = 400 + 250 + 40 = 690 [out of $780]
4 + 5 + 2 = 11 [out of 20 bills]
So now we can easily find out she had 9 bills of tens - because 20 - 11 = 9 or because (780 - 690) ÷ 10 = 90 ÷ 10 = 9.
Answer:
b. 600
Step-by-step explanation:
subtract money from parents from tuition
divide by months
The greatest common factor of 64 and 96 is... uhh... hmm... 32! Because 64/32 is 2, and 96/32=3. 2 and 3 have no factors in common, except 1.
The answer is 32(2+3).
This means 32*2 + 32*3
this is the same as 64+96