Math 116 Calculus

Question

let f(x) be a differentiabke function where

f(2)=5

F(8)=9

F prime (2)= -3

F prime (8)=6

find g prime (2) if g(x)=f(4x)

Answer 1

We are given the following:

f(2) = 5

f(8) = 9

f'(2) = -3

f'(8) = 6

We want to find g'(2).

We are told g(x) = f(4x).

By the chain rule, we have

g'(x) = 4f'(4x)

Then, we have

g'(2) = 4 * f'(4 * 2) = 4 * f'(8) = 4 * 6 = 24

Answer 2