Question

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)?

Answer 1

The table is attached in the figure.

    g(x) = f(4x) ⇒⇒⇒ differentiating both sides with respect to x

∴  g'(x) = $\frac{d}{dx} [f(x)] * \frac{d}{dx} [4x]=4*f'(x)$ ⇒⇒⇒⇒⇒⇒ chain role

To find g '(0.1)

Substitute with x = 0.1

from table: 

f'(0.1) = 1 ⇒ from the table

∴  g'(0.1) = 4 * [ f'(0.1) ]  = 4 * 1 = 4