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
The answers are:
1
2
4
cannot be determined
I got 1 please let me know if this is right or wrong!

Answer 1

g(x)=f(2x)
g'(x)=f'(2x)*2
g'(0.1)=f'(0.2)*2=2*2=4

for example, suppose f(x)=5x^2
Then f'(x) = 10x, as in the table.

Then g(x) = f(2x)=5(2x)^2=20x^2
g'(x) = 40x
g'(.1)=40*.1=4
g'(1) = f'(2)*2 = 2*2=4

Answer 2

f is a differentiable function on the interval [0, 1] and g(x) = f(4x). 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
–16
–4
4
Cannot be determined