Question

F(x) and g(x) are a differentiable function for all reals and h(x) = g[f(3x)]. The table below gives selected values for f(x), g(x), f '(x), and g '(x). Find the value of h '(1). (4 points)

x 1 2 3 4 5 6
f(x) 0 3 2 1 2 0
g(x) 1 3 2 6 5 0
f '(x) 3 2 1 4 0 2
g '(x) 1 5 4 3 2 0

Answer 1

15

Explanation:

took the test

Answer 2

`h'(x)=\Big[g\big(f(3x)\big)\Big]'=g'\big(f(3x)\big)\cdot\big[f(3x)\big]'=\\\\=g'\big(f(3x)\big)\cdot f'(3x)\cdot(3x)'=\boxed{g'\big(f(3x)\big)\cdot f'(3x)\cdot3}`

so:


`h'(1)=g'\big(f(3\cdot1)\big)\cdot f'(3\cdot1)\cdot3=g'\big(f(3)\big)\cdot f'(3)\cdot3=\\\\=g'(2)\cdot 1\cdot3=5\cdot 1\cdot3=\boxed{15}`