Help with Calc please!

Question

f is a differentiable function on the interval [0, 1] and g(x) = f(2x). The table below gives values of f '(x). What is the value of g '(0.1)? 

x

0.1

0.2

0.3

0.4

0.5

f '(x)

1

2

3

-4

5

Options:

1)	1
2)	2
3)	4
4)	Cannot be determined

Answer 1

g(x) = f(2x)

By the chain rule, g'(x) = f'(2x)[2x]' = 2f'(2x)

So, g'(0.1) = 2f'(0.2) = 2(2) = 4