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2. f is a differentiable function on the interval [0, 1] and g(x) = f(3x). The table below gives values of f '(x). What is the value of g '(0.1)? (4 points)
x 0.1 0.2 0.3 0.4 0.5
f '(x) 1 2 3 -4 5

A 1
B 3
C 9
D Cannot be determined

Respuesta :

LammettHash
Chain rule:

[tex]g(x)=f(3x)\implies g'(x)=3f'(3x)[/tex]

so

[tex]g'(0.1)=3f'(0.3)=3(3)=9[/tex]

Answer:

Option C.

Step-by-step explanation:

It is given that f is a differential function on the interval [0, 1].

[tex]g(x)=f(3x)[/tex]

Differentiate with respect to x.

[tex]g'(x)=f'(3x)\dfrac{d}{dx}(3x)[/tex]

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

We need to find the value of f'(0.1).

Substitute x=0.1 in the above equation.

[tex]g'(0.1)=3f'(3(0.1))[/tex]

[tex]g'(0.1)=3f'(0.3)[/tex]

From the given table it is clear that f'(0.3)=3.

[tex]g'(0.1)=3(3)[/tex]

[tex]g'(0.1)=9[/tex]

The value of g'(0.1) is 9.

Therefore, the correct option is C.

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