f(x) and g(x) are a differentiable function for all reals and h(x) = g[f(2x)]. The table below gives selected values for f(x), g(x), f '(x), and g '(x). Find the value of h '(1) ...

Question

f(x) and g(x) are a differentiable function for all reals and h(x) = g[f(2x)]. The table below gives selected values for f(x), g(x), f '(x), and g '(x). Find the value of h '(1)

f(x) and g(x) are a differentiable function for all reals and h(x) = g[f(2x)]. The table below gives selected values for f(x), g(x), f '(x), and g '(x). Find the value of h '(1)

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

x 1 2 3 4 5 6

Answer 1

For h'(1), x = 1.

If h(x) = g[f(2x)], due to the chain rule, h'(x) = g'[f(2x)]*f'(2x).

Therefore, h'(1) = g'[f(2)]*f'(2).

From the table, f(2) = 3 & f'(2) = 2.

Now, h'(1) = g'[3]*2.

From the table, g'(3) = 4.

Putting it all together, h'(1) = 4*2 = 8.

h'(1) = 8