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Let f(x) be a continuous and differentiable function on theinterval, 0<_ x<_ 1, and let g(x)=f(3x). The table below gives the values of f'(x), the derivatives of f(x). What is thevalue of g'(0.1)?
x 0.1 0.2 0.3 0.4 0.5 0.6
f'(x) 1.01 1.041 1.096 1.179 1.298 1.486

Respuesta :

lublana

Answer:

[tex]g'(0.1)=3.288[/tex]

Step-by-step explanation:

We are given that f(x) be a continuous and differentiable function on interval [0,1]

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

We have to find the value of g'(0.1)

Differentiate w.r.t x

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

Substitute x=0.1

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

Substitute the value of f'(0.3) from given table

[tex]g'(0.1)=3(1.096)[/tex]

[tex]g'(0.1)=3.288[/tex]

Hence, the value of g'(0.1)=3.288

saleemalij05

Answer:it is b

Step-by-step explanation:

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