Answer:
See Below.
Step-by-step explanation:
We want to show that the function:
![f(x) = e^x - e^{-x}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20e%5Ex%20-%20e%5E%7B-x%7D)
Increases for all values of <em>x</em>.
A function is increasing whenever its derivative is positive.
So, find the derivative of our function:
![\displaystyle f'(x) = \frac{d}{dx}\left[e^x - e^{-x}\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%5Be%5Ex%20-%20e%5E%7B-x%7D%5Cright%5D)
Differentiate:
![\displaystyle f'(x) = e^x - (-e^{-x})](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%20e%5Ex%20-%20%28-e%5E%7B-x%7D%29)
Simplify:
![f'(x) = e^x+e^{-x}](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20e%5Ex%2Be%5E%7B-x%7D)
Since eˣ is always greater than zero and e⁻ˣ is also always greater than zero, f'(x) is always positive. Hence, the original function increases for all values of <em>x.</em>
Dylan will pay 75% of the original price.
The equation that models the relationship between the amount of money Sarah has left is 55- 0.65x= y
17,604 points/36 shirts=<span>489 points per shirt
</span>82 shirts*489 points=<span>40,098 points</span>
The answer would be -9 -15n because you would be adding one to the -10 to the one and -9 and plus -2 and plus negative for any equals 15n