Answer:
![\displaystyle F'(0) = 15](https://tex.z-dn.net/?f=%5Cdisplaystyle%20F%27%280%29%20%3D%2015)
Step-by-step explanation:
We are given that:
![f'(0) = 5 \text{ and } F(x) = f(3x)](https://tex.z-dn.net/?f=f%27%280%29%20%3D%205%20%5Ctext%7B%20and%20%7D%20F%28x%29%20%3D%20f%283x%29)
And we want to find F'(0).
First, find F(x):
![\displaystyle F'(x) = \frac{d}{dx}\left[ f(3x)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20F%27%28x%29%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%5B%20f%283x%29%5D)
From the chain rule:
![\displaystyle \begin{aligned} F'(x) &= f'(3x) \cdot \frac{d}{dx} \left[ 3x\right] \\ \\ &= 3f'(3x)\end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbegin%7Baligned%7D%20F%27%28x%29%20%26%3D%20f%27%283x%29%20%5Ccdot%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cleft%5B%203x%5Cright%5D%20%5C%5C%20%5C%5C%20%26%3D%203f%27%283x%29%5Cend%7Baligned%7D)
Then:
![\displaystyle \begin{aligned} F'(0) & = 3f'(3(0)) \\ \\ & = 3f'(0) \\ \\ & = 3(5) \\ \\ & = 15\end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbegin%7Baligned%7D%20F%27%280%29%20%26%20%3D%203f%27%283%280%29%29%20%5C%5C%20%5C%5C%20%26%20%3D%203f%27%280%29%20%5C%5C%20%5C%5C%20%26%20%3D%203%285%29%20%5C%5C%20%5C%5C%20%26%20%3D%2015%5Cend%7Baligned%7D)
In conclusion, F'(0) = 15.
Answer:
B. 1
Step-by-step explanation:
I used a calculator
Answer:
A
Step-by-step explanation:
y-int = -2
so the line should cross (0, -2)
Rise over run is 2/5 so go up 2, over 5 and put your dot etc...
Answer:
I believe it is 11 1/4. Hope I'm right.
Step-by-step explanation:
I multiplied 2*5=10
Then I multiplied 1/4*5= 1 1/4
Then I added 10+1 1/4=11 1/4
Answer:
b
Step-by-step explanation:
its going up so its increasing between -8 and -4