Question

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

Answer 1

Answer:

$g'(0.1)=3.288$

Step-by-step explanation:

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

$g(x)=f(3x)$

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

Differentiate w.r.t x

$g'(x)=3f'(3x)$

Substitute x=0.1

$g'(0.1)=3f'(3(0.1))=3f'(0.3)$

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

$g'(0.1)=3(1.096)$

$g'(0.1)=3.288$

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

Answer 2

Answer:it is b

Step-by-step explanation: