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

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XKelvinidn

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]

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