Question

Use the following table to find the value of h '(2) if h(x) = f[g(x)]:

x 2 3 4
f(x) 5 1 6
g(x) 4 2 3
f'(x) 1 7 8
g'(x) 3 1 2

(A) 6
(B) 24
(C) 20
(D) 3

Answer 1

To find h'(2), we use the chain rule h'(x) = f'[g(x)] × g'(x). After obtaining the values from the provided table, we get h'(2) = f'[g(2)] × g'(2) = 8 × 3 = 24.

Step-by-step explanation:

The student is asking to find the value of h'(2) given h(x) = f[g(x)] and the values of f(x), g(x), f'(x), g'(x) at specific points. To find h'(2), we use the chain rule of differentiation: h'(x) = f'[g(x)] × g'(x). First, we find the value of g(2), then we use it to find f'[g(2)], and finally, we multiply that result by g'(2).

According to the given table:

• g(2) = 4
• f'(4) = 8 (since the table gives f'(x) and g(2) = 4)
• g'(2) = 3

Now, apply the chain rule: h'(2) = f'[g(2)] × g'(2) = 8 × 3 = 24.