Answered

At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

If f'(0) = 5 and F(x) = f(3x), what is F'(0)?

Sagot :

xKelvin

Answer:

[tex]\displaystyle F'(0) = 15[/tex]

Step-by-step explanation:

We are given that:

[tex]f'(0) = 5 \text{ and } F(x) = f(3x)[/tex]

And we want to find F'(0).

First, find F(x):

[tex]\displaystyle F'(x) = \frac{d}{dx}\left[ f(3x)][/tex]

From the chain rule:

[tex]\displaystyle \begin{aligned} F'(x) &= f'(3x) \cdot \frac{d}{dx} \left[ 3x\right] \\ \\ &= 3f'(3x)\end{aligned}[/tex]

Then:

[tex]\displaystyle \begin{aligned} F'(0) & = 3f'(3(0)) \\ \\ & = 3f'(0) \\ \\ & = 3(5) \\ \\ & = 15\end{aligned}[/tex]

In conclusion, F'(0) = 15.

Answer:

F'(0)=15

Step-by-step explanation:

Differentiate [tex]F(x)[/tex] with respect to [tex]x[/tex].

[tex]F'(x)=3f'(x)[/tex]

Subsitute [tex]0[/tex] for [tex]x[/tex] in the above equation.

[tex]F'(0)=3f'(0)\\=3\cdot5\\=15[/tex]

We hope this was helpful. Please come back whenever you need more information or answers to your queries. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.