Question

use the chart to find ( h(3) ) in simplest form.

h(x)=f(x)+g(x)

answer

( h(3)= )

Explanation:

Step1: Apply sum rule of derivatives

The sum rule states that if \(h(x)=f(x)+g(x)\), then \(h^{\prime}(x)=f^{\prime}(x)+g^{\prime}(x)\).

Step2: Substitute \(x = 3\)

Substitute \(x = 3\) into \(h^{\prime}(x)\). So \(h^{\prime}(3)=f^{\prime}(3)+g^{\prime}(3)\).
From the table, \(f^{\prime}(3)=-4\) and \(g^{\prime}(3)=8\).
Then \(h^{\prime}(3)=-4 + 8\).

Answer:

\(4\)