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

-16

Explanation:

I just took the test.

Answer 2

The table is attached in the figure.

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

∴ g'(x) =
`(d)/(dx) [f(x)] * (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