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 '(0.2)?

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 '(0.2)? 

x 0.1 0.2 0.3 0.4 0.5

f '(x)

1

2

3

-4

5

A)2

B)-8

C)4

D)Cannot be determined

Answer 1

Given g(x) = f(2x), if we differentiate both sides with respect to x, we obtain

g'(x) = f"(2x) * (2x)' = f'(2x) * 2, by the Chain Rule.

Therefore, g'(0.2) = f'(2 * 0.2) * 2 = f'(0.4) * 2 = -4 * 2 = -8.

The correct answer is B.