Question

use the chart to find $h(4)$ in simplest form.

$h(x)=8f(x)$

answer

$h(4)=$

Explanation:

Step1: Apply the constant multiple rule

The constant multiple rule states that if \(h(x) = cf(x)\), then \(h'(x)=cf'(x)\). Here \(c = 8\) and \(h(x)=8f(x)\), so \(h'(x)=8f'(x)\).

Step2: Substitute \(x = 4\)

We know from the table that \(f'(4)=- 12\). Substitute \(x = 4\) into \(h'(x)\): \(h'(4)=8\times f'(4)\).

$$h'(4)=8\times(-12)$$

Answer:

\(-96\)