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Andru [333]
3 years ago
5

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

Mathematics
2 answers:
Norma-Jean [14]3 years ago
8 0

Answer:

F'(0)=15

Step-by-step explanation:

Differentiate F(x) with respect to x.

F'(x)=3f'(x)

Subsitute 0 for x in the above equation.

F'(0)=3f'(0)\\=3\cdot5\\=15

Llana [10]3 years ago
7 0

Answer:

\displaystyle F'(0) = 15

Step-by-step explanation:

We are given that:

f'(0) = 5 \text{ and } F(x) = f(3x)

And we want to find F'(0).

First, find F(x):

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

From the chain rule:

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

Then:

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

In conclusion, F'(0) = 15.

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