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nirvana33 [79]
4 years ago
7

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 valu

e of g '(0.1)?

Mathematics
1 answer:
polet [3.4K]4 years ago
5 0

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

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