Question

use the chart to find ( h(4) ) in simplest form. ( h(x)=8 f(x) )

Explanation:

Step1: Apply the constant multiple rule

If \(h(x) = k\cdot f(x)\) (where \(k\) is a constant), then \(h^{\prime}(x)=k\cdot f^{\prime}(x)\). Here \(k = 8\) and \(h(x)=8f(x)\), so \(h^{\prime}(x)=8f^{\prime}(x)\).

Step2: Substitute \(x = 4\)

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

Answer:

\(h^{\prime}(4)=8\times(-12)=-96\)