Question

use the chart to find ( h(2) ) in simplest form.

h(x)=f(x) cdot g(x)

Explanation:

Step1: Apply the product rule

The product rule states that if \(h(x)=f(x)\cdot g(x)\), then \(h'(x)=f'(x)g(x)+f(x)g'(x)\).

Step2: Substitute \(x = 2\)

Substitute \(x = 2\) into the derivative formula. We know that \(f(2) = 12\), \(f'(2)=- 4\), \(g(2)=-8\), and \(g'(2)=-3\).
So \(h'(2)=f'(2)g(2)+f(2)g'(2)\).

Step3: Calculate the value

$$
LATEXBLOCK0
$$

Answer:

\(-4\)